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If $G$ is an abelian group of order 72, do we know how many subgroups of order 8 it has?

Just because it's a divisor doesn't mean that there is a subgroup of that size. But I'm wrong. Why?

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    Take a look at the [Sylow theorems](http://en.wikipedia.org/wiki/Sylow_theorems).2012-10-02

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