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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?
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?