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If you look at my answer to this question,this question, you will see that the number of proper subgroups grows at least as fast as $2^{n^2/6},$ so much faster than $n!.$ This is a result of Laci Pyber.

If you look at my answer to this question, you will see that the number of proper subgroups grows at least as fast as $2^{n^2/6},$ so much faster than $n!.$ This is a result of Laci Pyber.

If you look at my answer to this question, you will see that the number of proper subgroups grows at least as fast as $2^{n^2/6},$ so much faster than $n!.$ This is a result of Laci Pyber.

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Igor Rivin
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If you look at my answer to this question, you will see that the number of proper subgroups grows at least as fast as $2^{n^2/6},$ so much faster than $n!.$ This is a result of Laci Pyber.