Cohen and Lenstra made influential conjectures regarding the average value of the n-torsion of class groups of quadratic fields. So far these conjectures have been proven only for a very select number of values of n, namely n = 2^k or n = 3. In this talk, we sketch how to obtain asymptotics for the average 6-torsion. This is joint work with Robert Lemke Oliver, Efthymios Sofos and Frank Thorne.