There is a definition which help us to understand the semi-direct product well:
Let $K$ be a subgroup of a group $G$. Then a subgroup $Q\leq G$ is a complement of $K$ in $G$ if $K\cap Q=1$ and $KQ=G$.
Habitually, whenever I see the form $KQ=G$, I think of one of the subgroups $K$ or $Q$ are at least normal in group. But in the definition above J.J.Rotman quoted that $K$ is not necessarily normal in $G$ and moreover he didn't say anything about normality for $Q$ as well.
May I ask you to present me an example, having two subgroups not normal in $G$, and yet $G=KQ$? And if I misunderstand about above, please tell me. Thanks.