Let $(N \subset M)$ be an irreducible finite depth ($>2$) finite index inclusion of hyperfinite ${\rm II}_1$ factors, then for $n$ sufficiently large the subfactor $(N \subset M_n)$ is depth $2$ (*reducible*) and is isomorphic to $(R^H \subset R)$ with $H$ a weak Kac algebra (also called quantum groupoid, see prop. 9.1.1 p37 here). Then the initial subfactor is isomorphic to an intermediate of $(R^H \subset R)$ and by Galois correspondence (see here), it is completely given by the inclusion $(J \subset H)$ with $J$ a left coideal subalgebra of $H$.

*Question*: what are the applications of this result to the subfactors theory?

(In what this help to better understand the subfactors?)