abstract algebra - For the following group how to prove no two of them are isomorphic?

The groups are $A_3 \times \mathbb Z_2$, $A_4 \times \mathbb Z_2$, $\mathbb Z_8$, $S_3 \times \mathbb Z_4$. I know that if the order of the groups are not same it is not isomorphic. And the groups with huge order is not isomorphic to small groups. But I dont know how to determine whether the above groups are isomorphic to each other.