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

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# Homework Help: Subgroups of S4

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