# Definition:Inner Semidirect Product

## Definition

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 $G = H \ltimes N$.