The Controversy
Korach the son of Yitzhar the Levi, began a rebellion, separating and dissociating himself and his family from the congregation, persisting in a dispute to contest the appointment of Aaron to the kehunah. He banded with Dasan and Aviram, the sons of Eliav and On the son of Peles all from the tribe of Reuben who were neighbors with the Levim from the family of Kohas as they all lived on the South side of camp. Together they joined Korach's rebellion as the saying goes "Woe to the wicked, and woe to his neighbor!"
Korach went ahead and attracted the heads of the Sanhedrin to his cause though his convincing words.
Korach was drawn into the rebellion out of his jealousy towards his cousin Elizaphan the son of Uzziel who had been appointed by Moshe as the Nasi over the family of Kahas by the order of Hashem. Kehus had four sons; Amram who was the first had his two sons raised to greatness, Moshe being the king and Aharon being the Kohen Gadol. Yitzhar was the second son and it was only fitting that his son Korach receive the position of Nassi. Instead this position was given to Elizaphan the son of Uzziel the youngest son of Kahas.
 Son of Levi
Korach's lineage is cited as being the son of Yitzhar, the son of Kohas, the son of Levi. It does not extend to mention Yackov the father of Levi since he prayed that his name not be mentioned in connection with their quarrel. However when the genealogy of Levim serving on the Temple platform is traced Yackov's name is mentioned.