My question: I was asked to give a subgroup of order 6 of the permutation group S4. That part is not so difficult, for example S3 has order 6 and is a subgroup of S4. But now I have to show how many subgroups of order 6 are in S4. Intuitively thinking, there are four of them, each of them leaving 1, 2, 3 or 4 fixed. But how can you prove this?