Let $H,K$ be two subgroups of a group $G$ and let $A=H\cap K$ and $B$ be the subgroup of $G$ generated by $H$ and $K$. We know that \begin{array}{rcl} A & \rightarrow & H \\ \downarrow & & \downarrow \\ K & \rightarrow & G \end{array} is a pull-back square (morphisms are inclusions).
Does there exists a similar interpretation for $B$?