I'm looking for something like a Grassmannian, but which parameterizes the submodules of a module rather than the subspaces of a vector space. Most specifically, I'm looking for something which parameterizes the submodules of specifically Z^n. So another way to say it is that I'm looking for a space parameterizing for the subgroups of a free abelian group. (A moduli space?)

I've seen some references to the concept of a "Grassmannian of submodules" here and there (like the papers on the first page of https://www.google.com/search?q=%22grassmannian+of+submodules%22) but can't figure out if this handles modules like Z^n or not.

Does anyone know if such an object exists and if so, how to construct it? Where I can get more information on this?