Nonisomorphic groups of order 12. I'm trying to find 4 groups of order 12, none of which are isomorphic to each other.  Should I be trying external direct products? 
So far I have $A_4, \mathbb Z_{12},\,$ and $\,\mathbb Z_6\times \mathbb Z_2.\,$ How do I show all of these are non-isomorphic to each other? And how do I find a fourth?
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Yes, external direct product is need. You can get $A_4$ and $Z_2\times S_3$ are not isomorphic. 
And you can get all groups in abelian case easily.
