Let k be a number field, p a prime, and knr,p the maximal unramified p-extension of k. Golod and Shafarevich focused the study of knr,p/k on Gal(knr,p/k). Let S be a set of primes of k (infinite or finite), and kS the maximal p-extension of k unramified outside S. Nigel Boston and C.R. Leedham-Green introduced a method that computes a presentation for Gal(kS/k) in certain cases. Taking S={(1)}, Michael Bush used this method to compute possibilities for Gal(knr,2/k) for the imaginary quadratic fields k=Q(−2379),Q(−445),Q(−1015), and Q(−1595). In the case that k=Q(−2379), we illustrate a method that reduces the number of Bush's possibilities for Gal(knr,2/k) from 8 to 4. In the last 3 cases, we are not able to use the method to isolate Gal(knr,2/k). However, the results in the attempt reveal parallels between the possibilities for Gal(knr,p/k) for each field. These patterns give rise to a class of group extensions that includes each of the 3 groups. We conjecture subgroup and quotient group properties of these extensions