  A pre-subgroup of a multiplicative unitary $V$ on a finite dimensionnal
Hilbert space $H$ is a vector line $L$ in $H$ such that $V(L\otimes L)=L\otimes
L$. We show that there are finitely many pre-subgroups, give a Lagrange theorem
and generalize the construction of a `bi-crossed product'. Moreover, we
establish bijections between pre-subgroups and coideal subalgebras of the Hopf
algebra associated with $V$, and therefore with the intermediate subfactors of
the associated (depth two) inclusions. Finally, we show that the pre-subgroups
classify the subobjects of $(H,V)$.
