The split begins in the first chapter when Jack determines, at the end of the chapter, that the next time he encounters a pig, he will not hesitate to kill it, or even before that, with the first election. But by chapter 9 and the killing of Simon, the split is complete. Jack has appointed himself the Chief of his group and he runs the group with an iron fist. Jack asks who will come join his group. He promises them food, protection from the beast, and fun - the three things the boys want most. He has all but a few littluns, Sam and Eric, Piggy, and Ralph. Jack's style of command is very different from Ralph's. Jack rules with complete authority. He gives commands whereas Ralph tried to appeal to reason in order to get cooperation. Jack exerts his authority over the boys with threats of punishment for any perception of disobedience. To prove his authority, he beats one child - Wilfred - for no reason at all. Ralph would never do that because it lacks reason. By the beginning of chapter 10, the boys are completely divided and Jack's side is completely savage.
It is in Chapter 4, when the boys miss a chance for rescue, that the two groups' differences emerge most definitively. Jack and his hunters chase and kill a pig, and in the process, let the signal fire go out. Ralph's group is livid at this oversight, because they notice a boat out in the ocean that could have been their chance for rescue.
The standoff between the two groups that occurs afterwards shows the fundamental differences between each group's values. Jack's group prioritizes power and the hunt, while Ralph's group prioritizes order and the importance of rescue. This difference between them will have disasterous consequences.