On finiteness of the set of intermediate subfactors

For type $II_1$ factors $N\subset L$ with $[L:N]<\infty$, we show that the sets $\mathcal{L}_1=\{M\in \mathcal{L}(N\subset L)\colon N'\cap L \subset M\}$ and $\mathcal{L}_2=\{M\in \mathcal{L}(N\subset L)\colon N'\cap L =M'\cap L\}$ are finite. Moreover, $\mathcal{L}(N\subset L)$, the set of intermediate subfactors, is finite if and only if it is equal to $\mathcal{L}_1\cup \mathcal{L}_2$. If $N$ is an irreducible subfactor, then we recover a result of Y. Watatani.