Abstract: In 1971, Davenport and Heilbronn prove the celebrated theorem determining the average of 3-torsion in class groups of quadratic extensions. In this talk, we will study 3-torsion in class groups of 2-extensions, which are towers of relative quadratic extensions. As an example, we determine the average of 3-torsion in class groups of D_4 quartic extensions. This is a joint work with Robert J. Lemke Oliver and Melanie Matchett Wood.