The title pretty much says it all... anyway... let $G$ be a semi-direct product of $N$ by $Q$, and let $H$ be a subgroup of $G$.
Can one always find subgroups $N_1$ and $Q_1$, of $N$ and $Q$ respectively, such that $H$ is the semi-direct product of these two groups?
If not in general, can one say anything about the following cases:
i) $G = \text{GL}(n,K)$, i.e. the general linear group of dimension $n$ over some field $K$
ii) $G = \text{Aff}(E)$, i.e. the group of all affine motions of some (finite dimensional) linear space
thx in advance