Topological order for translation invariant Pauli stabilizer models in two dimensions is well-understood due to a structure theorem by Haah, which states that all such models are equivalent to copies of Toric code. In two dimensions, there is an S-matrix invariant that encodes the topological data about commutation between string logical operators and equivalently, braiding between topological excitations. In three dimensions, much less is understood due to the existence of Fracton Topological order. I will discuss commutation quantities which are inspired by the S-matrix invariant in 2D but can be employed for stabilizer models in 3D to coarsely classify them into TQFTs, foliated and fractal Type-I models with rigid string operators and Type-II models with no string operators. I will also briefly discuss Entanglement Renormalization group flow of stabilizer models which will inspire conjectures for a structure theorem in three dimensions.