  Let (k1,k2,k3,k4) be a quartet of cyclic cubic number fields sharing a common
conductor c=pqr divisible by exactly three prime(power)s p,q,r. For those
components k of the quartet whose 3-class group Cl(3,k) = Z/3Z x Z/3Z is
elementary bicyclic, the automorphism group M = Gal(F(3,2,k)/k) of the maximal
metabelian unramified 3-extension of k is determined by conditions for cubic
residue symbols between p,q,r and for ambiguous principal ideals in subfields
of the common absolute 3-genus field k* of k1,k2,k3,k4. With the aid of the
relation rank d2(M), it is decided whether M coincides with the Galois group G
= Gal(F(3,infinity,k)/k) of the maximal unramified pro-3-extension of k.
