Proving Non-Isomorphism: Subgroup and Dihedral Group of Equal Order

[physix123]

how would you go about showing that a subgroup and dihedral group- of the same order- are not isomorphic?

 

[daveyinaz]

Counterexample.

 

[HallsofIvy]

Sub group of WHAT? The "dihedral group" of a specified order is the reflection and rotations group of a polygon but you would have to say what subgroup, of what group you want to show is not isomorphic to that. I imagine there must exist SOME subgroup, of SOME group, that is isomorphic to a dihedral group. Did you mean to say, "show that a subgroup of a dihedral group cannot be isomorphic to another dihedral group"?