Why cant D_n be isomorphic to the external direct product of these two groups?

Question

Dihedral group D_n of order 2n, (n>or=3), has subgroup of n rotations and a subgroup of order 2.

Answer 1

Well, there's the minor issue that the direct product of two cyclic groups is always abelian, whereas for n≥3, D_n is not.