The type of the classifying space for a family of subgroups

The classifying space for a family of subgroups of a group Γ is defined up to Γ-homotopy as a Γ-CW-complex such that is contractible if H belongs to and is empty otherwise. We investigate the question whether there is a finite-dimensional Γ-CW-model, a finite Γ-CW-model or a Γ-CW-model of finite type for focusing on the case where is the family of finite subgroups.