Let N⊂M be an irreducible inclusion of type type II1 factors
with finite Jones index. We shall introduce the notion of normality for
intermediate subfactors of the inclusion N⊂M. If the depth of N⊂M is 2, then an intermediate subfactor K for N⊂M is normal
in N⊂M if and only if the depths of N⊂K and K⊂M
are both 2. In particular, if M is the crossed product N⋊G of a
finite group G, then K=N⋊H is normal in N⊂M if and only
if H is a normal subgroup of G.Comment: 25 pages, amslatex, to appear in J. Math. Soc. Japa