  For any abstract subfactor planar algebra $P$, there exists a finite index
extremal subfactor $M_0 \subset M_1$ with $P$ as its standard invariant. In
this paper, we classify the automorphism group of a bipartite graph planar
algebra, and obtain subfactor planar subalgebras by taking fixed points under
groups of automorphisms. This construction provides both new examples of
subfactors and new descriptions of the planar algebras of previously known
examples.
