A subfactor $N \subset M $ is maximal if it admits no non-trivial intermediate subfactors $N \subset P \subset M $.

**Question**: Are there only finitely many maximal irreducible amenable subfactors at fixed finite index (up to isomorphism)?

*Bonus question*: let $\alpha$ the index of a irreducible amenable subfactor.

Is there a maximal irreducible amenable subfactor of index $\alpha$ ?

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