  The isomorphism type of the Galois group of the 2-class field tower of
quadratic number fields having a 2-class group with abelian type invariants
(4,4) is determined by means of information on the transfer of 2-classes to
unramified abelian 2-extensions, collected in the Artin pattern. In recent
investigations by Benjamin and Snyder, the length of the tower of such fields
has turned out to be dependent on the rank of the 2-class group of the first
Hilbert 2-class field. Significant progress is achieved by extending the pool
of possible metabelian 2-groups of the second Hilbert 2-class field from the
SmallGroups database, resp. Hall-Senior classification, with the aid of the
p-group generation algorithm, and sifting the pool by means of pattern
recognition.
