# Dihedral Group - isomorphism

The dihedral group Dn of order 2n has a subgroup of rotations of order n and a subgroup of order 2. Explain why Dn cannot be isomorphic to the external direct product of two such groups.

${D}_n \not\cong \mathbb{Z}/2 \oplus \mathbb{Z}/n,$ as the latter is Abelian and the former is not.