"Adonijah conferred with Joab son of Zeruiah and with Abiathar the priest, and they gave him their support." NIV translation
Joab was the commander of the army and was David's right hand man. He probably would not have picked Solomon to replace David and, together with the priest, they supported Adonijah's power grab. This combination of the political and the religious leaders joining forces to go against the will of God happens today in many countries. It will become worldwide in the last days with the emergence of the unholy trinity (see Revelation 13).
"But Zadok the priest, Benaiah son of Jehoiada, Nathan the prophet, Shimei and Rei and David's special guard did not join Adonijah." NIV translation
Not everyone went along with Adonijah's plan. Zadok was descended from Aaron and would become the first high priest. Benaiah was one of the most famous and fearless soldiers in Israel. Nathan whose name means "He has given" was a prophet who was always willing to speak the truth as he had been the one to confront David with his sin with Bathsheba.
These men were willing to go against the tide and stand firm because they were strong men of God. All of them were close to the king and it is a reminder to us that we all need to have strong men and women of God close to us in our walk in this world.
"Adonijah then sacrificed sheep, cattle and fattened calves at the Stone of Zoheleth near En Rogel. He invited all his brothers, the king's sons, and all the men of Judah who were royal officials, but he did not invite Nathan the prophet or Benaiah or the special guard or his brother Solomon." NIV translation
Adonijah threw a party to announce himself as king but we can tell that it was not God's will as he offered sacrifices near En-Rogel instead of in Jerusalem. The Stone of Zoheleth (the serpent-stone) was a rocky plateau overlooking the Kidron Valley. The Gihon Spring was located there and was the main source of water for Jerusalem. The spring did not continuously flow and so a pool was built in Jerusalem to store water for the time when the fountain did not flow. The spring is also called the Virgin's Fountain as many believe that Mary washed Jesus' swaddling clothes there.