Let N and H be groups, and let G be an extension of H by N. In this article, we describe the structure of the complex group ring of G in terms of data associated with N and H. In particular, we present conditions on the building blocks N and H guaranteeing that G satisfies the zero-divisor and idempotent conjectures. Moreover, for central extensions involving amenable groups we present conditions on the building blocks guaranteeing that the Kadison–Kaplansky conjecture holds for the group C∗-algebra of G. © 2022, The Author(s).