  For any number field K with non-elementary 3-class group Cl(3,K) = C(3^e) x
C(3), e >= 2, the punctured capitulation type kappa(K) of K in its unramified
cyclic cubic extensions Li, 1 <= i <= 4, is an orbit under the action of S3 x
S3. By means of Artin's reciprocity law, the arithmetical invariant kappa(K) is
translated to the punctured transfer kernel type kappa(G2) of the automorphism
group G2 = Gal(F(3,2,K)/K) of the second Hilbert 3-class field of K. A
classification of finite 3-groups G with low order and bicyclic commutator
quotient G/G' = C(3^e) x C(3), 2 <= e <= 6, according to the algebraic
invariant kappa(G), admits conclusions concerning the length of the Hilbert
3-class field tower F(3,infty,K) of imaginary quadratic number fields K.
