Starting from , multiply both sides (on the left) by . Then multiply both sides (on the left) by x.

What that argument shows is that (order of b) ≤ (order of a). But if b is conjugate to a, then a is conjugate to b. So you can switch a and b in that argument, getting the reverse inequality.

It's probably best to start by looking at the orders of elements in these groups. is the only one to have an element of order 12, so that sets it apart from any of the other groups. In each of the remaining groups, is there an element of order 4? How many elements have order 6? By looking at questions like that, you can determine that some of the groups are nonisomorphic to others. If there are any groups that you cannot distinguish by properties like that, then you will have to think about whether they are in fact isomorphic.