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

Existence of the $AH+2$ subfactor