Wall's conjecture for maximal fusion subalgebras

Let ${\cal F}$ be a finite-dimensional semisimple fusion algebra with $n$ simple objects. A fusion subalgebra generated by a subset of the simple objects is maximal if it is maximal among proper fusion subalgebras of this form.

Fusion-algebra version of Wall's conjecture. The number of maximal fusion subalgebras generated by a subset of the simple objects of ${\cal F}$ is less than $n$.

The conjecture holds when ${\cal F}$ is commutative, by a result of D. Nikshych and V. Ostrik cited in the source. The general case is left open.