What does isomorphic mean?
If G1 and G2 are two groups, an isomorphism is a one-to-one function f (when g is not h, f(g) is not f(h)) defined on all the elements of G1 with values in G2 such that for every g, h in G1, f(g)f(h)=f(gh), and every element of G2 is the image of some element in G1. This means that from the point of view of formal group operations, G1 and G2 are the same. If two groups are isomorphic they must have the same number of elements, but, for example, A4 x Z2 and S4 both have 24 elements, yet they are not isomorphic.
