Suppose $G$ has a finite index subgroup $N$ such that $N$ acts properly and cocompactly on a CAT(0)-cube complex. Does $G$ also act properly and cocompactly on a CAT(0)-cube complex?

Edit: After searching the web a little I found that the answer to this question is no, in general. There exists for example a 3-dimensional torsion-free crystallographic group that does not act freely and cocompactly on a CAT(0)-cube complex. (see Example 16.11 in 'THE STRUCTURE OF GROUPS WITH A QUASICONVEX HIERARCHY', by Dani Wise).

So my new question becomes: what conditions can one impose on $G$, such that the answer to the original question is yes?