internal direct product question

if m>2, must ZmXDn and Dmn always have different isomorphic types? (where X= internal direct product).

If it were the external direct product of the two, I can easily see that Zm+Dn is not isomorphic to Dmn, however i am not sure what to do with the internal direct product. I know that a group G is equal to the internal direct product of two groups if both of the two groups are normal in G and thei intersection is equal to e. Would I need this fact for this problem?

Any help would be great, I am really struggle with the concept of the internal direct product in this problem.

Thanks