The group for of type.

Let denote the discriminant of a real quadratic field. For all bicyclic biquadratic fields , having a -class group of type , the possibilities for the isomorphism type of the Galois group of the second Hilbert -class field of are determined. For each coclass graph , , in the sense of Eick, Leedham-Green, Newman and O'Brien, the roots of even branches of exactly one coclass tree and, in the case of even coclass , additionally their siblings of depth and defect , turn out to be admissible. The principalization type of -classes of in its four unramified cyclic cubic extensions is given by for , and by for . The theory is underpinned by an extensive numerical verification for all fields with values of in the range , which supports the assumption that all admissible vertices will actually be realized as Galois groups for certain fields , asymptotically. [ABSTRACT FROM AUTHOR]