Almost simple group (reviewed)

An almost simple group is a group $G$ that lies between a non-abelian simple group $S$ and its automorphism group Aut$(S)$, i.e. $S \subseteq G \subseteq $Aut$(S).$

Every non-abelian simple group is almost simple, but it is not implied by $G$ being quasisimple, as shown by these examples.