If we are just looking at the story of Korah (and not what happens after he is dead), the conflict is resolved by God killing Korah, Dathan, and Abiram, along with their entire households.
In the story of Korah, the conflict is between him and his supporters on the one side and Moses and Aaron on the other. Korah and his supporters want a position of greater power. They think that Moses and Aaron have set themselves above the rest of the community.
When Moses hears this, he allows God to decide what should happen. God decides to kill Korah and his followers to show that he truly does favor Moses and Aaron. In this way, God resolves the conflict between the two groups.