Normal intermediate subfactors

Let N C M be an irreducible inclusion of type type 111 factors with finite Jones index. We shall introduce the notion of normality for intermediate subfactors of the inclusion N C M. If the depth of N C M is 2, then an intermediate subfactor K for N C M is normal in N C M if and only if the depths of N C K and K C M are both 2. In particular, if M is the crossed product N ><l G of a finite group G, then K = N ><l His normal in NC M if and only if His a normal subgroup of G.