In group theory, a metacyclic group is an extension of a cyclic group by a cyclic group. Equivalently, a metacyclic group is a group ${\displaystyle G}$ having a cyclic normal subgroup ${\displaystyle N}$, such that the quotient ${\displaystyle G/N}$ is also cyclic.

Metacyclic groups are metabelian and supersolvable. In particular, they are solvable.

A group ${\displaystyle G}$ is metacyclic if it has a normal subgroup ${\displaystyle N}$ such that ${\displaystyle N}$ and ${\displaystyle G/N}$ are both cyclic.

In some older books, an inequivalent definition is used: a group ${\displaystyle G}$ is metacyclic if ${\displaystyle [G,G]}$ and ${\displaystyle G/[G,G]}$ are both cyclic. This is a strictly stronger property than the one used in this article: for example, the quaternion group is not metacyclic by this definition.