---
tag: 0H3WZXCZNF
kind: concept
name: Semidirect product
msc: ["20E22"]
sources:
  - url: https://en.wikipedia.org/wiki/Semidirect_product
    locator: lead section
same_as:
  wikidata: Q291126
  wikipedia: Semidirect product
---

## Summary

A semidirect product builds a group from a group $N$ and a group $H$ that acts on $N$ by automorphisms.
It generalises the direct product, and $N$ becomes a normal subgroup of the result.