Group theory help...?

Equality of order isnt enough for the groups to be isomorphic (i think). Depending on the operation of the group Z3 x Z8, it may have an element (2,7) of order 14 while S4 has (1,2,3,4) as its highest order element. For the groups to be isomorphic, S4 would need an element of order 14, which it does not (not remembering this too well, but pretty sure the very first statement is true).