  We discuss the renormalization group in the context of gravitational theories
with independent metric and affine connection. Considering a class of theories
with both propagating torsion and nonmetricity, we perform an explicit
computation of one-loop divergences, starting from a simple yet
phenomenologically viable modification of the Yang--Mills-like action.
Similarly to what happens in Poincar\'e gauge theory, in addition to the
action, quadratic in curvature, torsion, and nonmetricity, many more terms are
generated. We correct a known result for the beta function of the Yang--Mills
term and show that considerations previously presented in the literature are
incomplete.
