\begin{definition}[Definition:Extension Problem]
Let $H$ and $K$ be groups.
The '''extension problem''' is to determine all groups $G$ such that:
:$K \trianglelefteq G$
:$G / K \cong H$
where:
:$K \trianglelefteq G$ denotes that $K$ is a normal subgroup of $G$
:$G / K$ denotes the quotient group of $G$ by $K$
:$\cong$ denotes group isomorphism.
\end{definition}