Definition:Extension Problem

Definition
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.