  If $G$ is a countable, discrete group generated by two finite subgroups $H$
and $K$ and $P$ is a II$_1$ factor with an outer G-action, one can construct
the group-type subfactor $P^H \subset P \rtimes K$ introduced in \cite{BH}.
This construction was used in \cite{BH} to obtain numerous examples of infinite
depth subfactors whose standard invariant has exotic growth properties. We
compute the planar algebra (in the sense of Jones \cite{J2}) of this subfactor
and prove that any subfactor with an abstract planar algebra of "group type"
arises from such a subfactor. The action of Jones' planar operad is determined
explicitly.

Operator Algebras;Quantum Algebra