In this paper we give a large number of quadratic fields Q(fd) whose
class group H(d) has 3-Sylow subgroup H3(d) with rank r3(d)> 1. They
include 20 discriminants d < 0 with r^(d)= 5. The associate real fields have r}(d')= 4. The distribution of the Hy(d) is studied and its relative
frequency is compared with the heuristic conjectures of Cohen and
Lenstra. Some of the H(d) are recorded since they are of special interest. Some related topics are also considered.