Wall's conjecture for intermediate subfactors

Let $N\subset M$ be an irreducible subfactor, meaning that $N'\cap M=\mathbb{C}$, with finite index. Let $M\subset M_1$ be the Jones basic construction, so that $N'\cap M_1$ is the second higher relative commutant. Wall's subfactor conjecture. The number of maximal intermediate subfactors between $N$ and $M$ is less than the dimension of $N'\cap M_1$. The conjecture generalizes Wall's conjecture because, for a crossed product by a finite group, maximal intermediate subfactors correspond to maximal subgroups and the dimension of the second higher relative commutant equals the group order. The source reports verification for several classes of subfactors, including examples from conformal field theory and those related to groups and Hopf algebras; the general finite-index case remains open.