  We compute all the moments of a normalization of the function which counts
unramified $H_{8}$-extensions of quadratic fields, where $H_{8}$ is the
quaternion group of order 8, and show that the values of this function
determine a constant distribution. Furthermore we propose a similar
modification to the non-abelian Cohen-Lenstra heuristics for unramified
G-extensions of quadratic fields for G in a large class of 2-groups, which we
conjecture will give finite moments which determine a distribution. Our method
additionally can be used to determine the asymptotics of the unnormalized
counting function, which we also do for unramified $H_{8}$-extensions.
