  We give two different proofs of the existence of the $AH+2$ subfactor, which
is a $3$-supertransitive self-dual subfactor with index $\frac{9+\sqrt{17}}{2}
$. The first proof is a direct construction using connections on graphs and
intertwiner calculus for bimodule categories. The second proof is indirect, and
deduces the existence of $AH+2$ from a recent alternative construction of the
Asaeda-Haagerup subfactor and fusion combinatorics of the Brauer-Picard
groupoid.
