Many believe there is only one group of 144,000 people. However, these quotes should make it clear that there is more than one group.

The First 144,000

From the following scriptures it seems fairly clear that the first 144,000 have to be sealed before the true time of tribulation begins. Later more people receive the same blessings as the 144,000

Revelation 7
1 AND after these things I saw four angels standing on the four corners of the earth, holding the four winds of the earth, that the wind should not blow on the earth, nor on the sea, nor on any tree. 2 And I saw another angel ascending from the east, having the seal of the living God: and he cried with a loud voice to the four angels, to whom it was given to hurt the earth and the sea, 3 Saying, Hurt not the earth, neither the sea, nor the trees, till we have sealed the servants of our God in their foreheads.
– Conspiracy Rising Ref. 23
4 And I heard the number of them which were sealed: and there were sealed an hundred and forty and four thousand of all the tribes of the children of Israel.
9 After this I beheld, and, lo, a great multitude, which no man could number, of all nations, and kindreds, and people, and tongues, stood before the throne, and before the Lamb, clothed with white robes, and palms in their hands; 10 And cried with a loud voice, saying, Salvation to our God which sitteth upon the throne, and unto the Lamb.

D&C 77
8 Q. What are we to understand by the four angels, spoken of in the 7th chapter and 1st verse of Revelation?
A. We are to understand that they are four angels sent forth from God, to whom is given power over the four parts of the earth, to save life and to destroy; these are they who have the everlasting gospel to commit to every nation, kindred, tongue, and people; having power to shut up the heavens, to seal up unto life, or to cast down to the regions of darkness.
9 Q. What are we to understand by the angel ascending from the east, Revelation 7th chapter and 2nd verse?
A. We are to understand that the angel ascending from the east is he to whom is given the seal of the living God over the twelve tribes of Israel; wherefore, he crieth unto the four angels having the everlasting gospel, saying: Hurt not the earth, neither the sea, nor the trees, till we have sealed the servants of our God in their foreheads. And, if you will receive it, this is Elias which was to come to gather together the tribes of Israel and restore all things.
11 Q. What are we to understand by sealing the one hundred and forty-four thousand, out of all the tribes of Israel—twelve thousand out of every tribe?
A. We are to understand that those who are sealed are high priests, ordained unto the holy order of God, to administer the everlasting gospel; for they are they who are ordained out of every nation, kindred, tongue, and people, by the angels to whom is given power over the nations of the earth, to bring as many as will come to the church of the Firstborn.

The Second 144,000

These are those who are chosen to travel from the Rockies to Missouri to build the city of Zion. Clearly, the time of tribulation has already started. This could be the same people as the first 144,000 but perhaps not.

The Third 144,000

This third group leaves from the city of Zion and/or Adam-Ondi-Ahman to preach to Israel, which is hidden among the Gentile nations. These are they who are called and sent forth during the time of the mark of the beast. Following close on their heals are the reaping angels.

Revelation 14
1 AND I looked, and, lo, a Lamb stood on the mount Sion, and with him an hundred forty and four thousand, having his Father’s name written in their foreheads. 2 And I heard a voice from heaven, as the voice of many waters, and as the voice of a great thunder: and I heard the voice of harpers harping with their harps: 3 And they sung as it were a new song before the throne, and before the four beasts, and the elders: and no man could learn that song but the hundred and forty and four thousand, which were redeemed from the earth. 4 These are they which were not defiled with women; for they are virgins. These are they which follow the Lamb whithersoever he goeth. These were redeemed from among men, being the firstfruits unto God and to the Lamb. 5 And in their mouth was found no guile: for they are without fault before the throne of God.

Brigham Young, Journal of Discourses Vol 7 Discourse 29
By-and-by, after you have fulfilled your missions to the nations of the Gentiles, and there will not any more of them repent—that is, when you have fully accomplished all that is required of you in relation to them, you will have another mission, and so will the Twelve, and that is to the house of Israel that may be among those nations; I mean the literal descendants of Jacob—the Jews, and the descendants of the other tribes that may be scattered among those nations. There are some from the ten tribes among them; but the body of the ten tribes are in the north country. You will find a few among all these Gentile nations: you will have to direct your attention to them after you have fulfilled your mission among the Gentiles, and their times are fulfilled. You will have something to do among the Jews, and then will be a time of great power, such as you and I have not dreamed of. Indeed, we could not, with our narrow comprehensions of mind, perceive the power that will then follow. The Lord has told it in a revelation in the Book of Doctrine and Covenants. He has told us, before the rise of this Church, that in bringing forth this Gospel, it is a light that could not be hid in darkness: therefore, he says, I must bring the fulness of my Gospel from among the Gentiles to the house of Israel; or, this light of the fulness of my Gospel will, as it were, be covered up and hid in darkness in many respects, and will not shine with that brilliancy, power, and greatness: it will not appear in that magnitude that it will when I bring it from the midst of the Gentiles to my people, O house of Israel. Again, the Lord says, in another revelation in the Book of Doctrine and Covenants, that when we have preached the Gospel faithfully to the Gentile nations, then cometh the day of my power; and we already know what the Psalmist says in regard to that day—”My people shall be willing in the day of my power.” The house of Israel have been unwilling in many generations past to receive the Gospel; but in the day of his power, you Seventies, that will go forth among the nations of Gentiles to hunt out the literal descendants of Jacob, will be armed with that glory, power, and majesty, and clothed upon from on high to that degree that no power on earth can stay you; and then, in that day, the seed of Jacob will be willing to receive the testimony of the Gospel. Then many of the Jews will believe, although many of that nation will gather to Jerusalem in unbelief.

Orson Pratt, Journal of Discourses Vol 18 Discourse 4
Chosen for what? To be sealed in their foreheads. For what purpose? So that the power of death and pestilence and plague that will go forth in those days sweeping over the nations of the earth will  have no power over them. These parties who are sealed in their foreheads will go forth among all people, nations and tongues, and gather up and hunt out the house of Israel, wherever they are scattered, and bring as many as they possibly can into the Church of the firstborn, preparatory to the great day of the coming of the Lord. One hundred and forty-four thousand missionaries! Quite a host.

The Fourth 144,000

This is the group that goes out from Jerusalem among the heathen nations to find the last  who are willing to repent. This will be a time of continual warfare in the final years before the battle of Armageddon.

Some notes on numerology

144,000 in base 60 is 40,0,0 which is a symbolic number meaning many thousands.
144,000 is also 12 (priesthood) squared (fullness of), multiplied by 1000 (completeness) So in biblical numerology, this number is symbolic of a fullness of the complete priesthood.