Homomorphic secret sharing schemes have been of fundamental importance in the development of secure multyparty protocols, like for example e-voting protocols. We propose a classification of homorphic schemes between three categories: Linear, abelian and nonabelian schemes. We study the information rates that can be achieved by those three types of schemes. We prove that nonabelian schemes outperform linear schemes, and we conjecture that the same is true for abelian schemes. We provide some strong evidence concerning the conjecture.