Section 7.6 Part 2

Difficult: I don't understand what the difference between parts (2)/(3) and (4)/(5) are in Theorem 7.34. I know that the book explained a bit after the theorem was given, but I don't understand what it means and why these statements are not saying the same thing.

Reflective: I think it's interesting that a subgroup has to be normal in order for Theorem 7.33 to work. I think that the concept of normal subgroups is interesting because it seems like it would be much more unlikely that many normal subgroups, except for the center, would exist in a large group.