There are many conflicts within the novel, but to point out three, they should be major conflicts.
The biggest conflict is between Ralph and Jack. This is an external conflict that exists between two characters. Ralph represents civilization while Jack represents savagery. The resolution to that occurs when the officer arrives just in time. Although it appeared that savagery won out, because of the officer, civilization won by rescuing the boys from killing themselves.
Another conflict was Piggy's conflict of fitting into the tribe. This could either be an internal conflict that he had--knowing that he would never fit in with Jack and the others of his tribe, or it could be looked at as Piggy against the entire hunting tribe of Jack's. That resolution was clear. Roger released the rock that killed Piggy. So Piggy lost.
The last conflict that stands out is Simon's conflict. He represents morals and values and realizes that the "beast" is really within them--not a physical threat somewhere in the forest. His conflict seems to be internal as well--or perhaps like Piggy's it is against all of the boys of Jack's tribe. None of them really seem to understand what the "beast" really is. Only Simon has a full awareness of what is happening on the island. This resolution also has a bad ending. But it is clear. Simon is killed while trying to explain that the "beast" was just a dead man on a mountain. Simon also loses like Piggy did.