Donovan's conjecture and extensions by the centralizer of a defect group

We consider Donovan's conjecture in the context of blocks of groups G with defect group D and normal subgroups N < G such that G = CD(D \ N)N, extending similar results for blocks with abelian defect groups. As an application we show that Donovan's conjecture holds for blocks with defect groups of the form Q8 x C2n or Q8 x Q8 dened over a discrete valuation ring.