Non-abelian subgroup of size 6 in A_6

[alex07966]

I need to find just one non-abelian subgroup of size 6 in A_6.

I have started by noting that the subgroup must be isomorphic to D_6 and then tried to use the permutations in D_6 that sends corners to corners. I then came across the problem that the reflection elements in D_6 consist of 2-cycles and hence are not elements of A_6.
I am now very stuck... please help :)

 

[Dick]

There's really only one nonabelian group of order 6, S_3. Can you think of a sort of natural way to find a copy of S_3 in A_6? Hint: interchange elements two at a time.

 

[alex07966]

Thanks a lot. I have found what the subgroup is now: {e, (23)(56), (13)(46), (12)(45), (123)(456), (132)(465)}. I need to justify my answer so I need to show that this is isomorphic to D_6 and therefore is a subgroup. I'll have a go.