\begin{definition}[Definition:Inner Semidirect Product]
Let $G$ be a group.
Let $H$ be a subgroup of $G$.
Let $N$ be a normal subgroup of $G$.
Let $H$ and $N$ be complementary.
Then $G$ is the '''inner semidirect product''' of $N$ and $H$.
This is denoted $G = N \rtimes H$ or $G = H \ltimes N$.
\end{definition}