Subgroups of generalized dihedral groups A generalized dihedral group, $D(H) := H \rtimes C_2$,  is the semi-direct product of an abelian group $H$ with a cyclic group of order $2$, where $C_2$ acts on $H$ by inverting elements.
I know that the total number of subgroups of $D(H)$ is the number of subgroups of $H$ plus the sum of subgroup indices of $H$ ($\sum_{L \leq H}[H : L]$).
But I'm not interested in the actual subgroups, I only need the structures of subgroups of $D(H)$ up to isomorphism. Naturally all the subgroups of $H$ are (normal) subgroups of $D(H)$ and for each $L \leq H$ also $D(L) \leq D(H)$. But is that all or can there be other structures as well?
I read about the subgroups of semi-direct products in general, but the situation seemed quite complicated. Would it be easier to find just the structures?

Let $K$ be a subgroup of $D(H)$. 
If $K$ is not contained in $H$, then $K$ contains some $g \not\in H$. Then $g$ is an involution and $D(H) = H \rtimes \langle g \rangle$. Hence $K = (H \cap K) \rtimes \langle g \rangle$ and $K \cong D(H \cap K)$.
