Abstract. Let k be a field and R a k-algebra. Given an R-module M and a natural number t, one may consider the set of all submodules of length t, say with prescribed composition factors. For t = 1, this just concerns the socle of M. The lecture is devoted to a discussion of the case t = 2 which already is tantalizing. The typical case to be studied concerns modules over a Kronecker algebra R.