In the book the boys basically split up into two groups, one with Jack and the other with Ralph. Could this be considered what went wrong on the island since it hindered the groups ability to survive, and Jack's group caused problems for Ralph's?

As the old saying goes "United we stand, divided we fall," and this is precisely what happens to the stranded schoolboys in Lord of the Flies. To survive in such a strange, hostile environment it's essential that the boys come together and help each other out, to work as a team to create a habitable living-space. At first, this is what they do, with each boy carrying out a specific duty such as hunting or gathering fuel for the fire.
But the initial good order soon degenerates into anarchy and chaos. The main problem is that, in the characters of Ralph and Jack, we have two powerful, charismatic personalities, each with his own vision of what life on the island should be like. The truth is that the island simply isn't big enough for the both of them, and so conflict is inevitable at some point. Ralph wants to create a rules-based order on the island. Only this way will the boys be able to thrive, as well as survive in their new surroundings. Jack, on the other hand, has no time for any of this. As far as he's concerned, might is right; he's determined to establish himself as sole ruler over the other boys, and woe betide anyone who gets in his way. These two conflicting personalities, these two conflicting visions, are simply irreconcilable, and their inevitable clash is largely responsible for the numerous problems that the boys encounter on the island.