Normal subgroups of symplectic groups over rings

We consider a module with an alternating form over a commutative ring. Under certain conditions, which hold, for example, when the form is nonsingular and the module is projective of rank 6 and contains a unimodular vector, we describe all subgroups of the symplectic group which are normalized by symplectic transvections. This generalizes many previous results of Dickson, Klingenberg, Abe, Bak, et al.