  This is the second part of a series of 3 papers. Using the same method and
the same coordinates as in part 1, rotating dust solutions of Einstein's
equations are investigated that possess 3-dimensional symmetry groups, under
the assumption that only one of the Killing fields is spanned on the fields of
velocity $u^{\alpha}$ and rotation $w^{\alpha}$, while the other two define
vectors that are linearly independent of $u^{\alpha}$ and $w^{\alpha}$ at every
point of the spacetime region under consideration. The Killing fields are found
and the Killing equations solved for the components of the metric tensor in
every case that arises. The Einstein equations are simplified in a few cases,
three (most probably) new solutions are found, and several classes of solutions
known earlier are identified in the present scheme. They include those by
Ozsv\'ath, Maitra, Ellis, King and Vishveshwara and Winicour.
  PACS numbers 04.20.-q, 04.20.Cv, 04.20.Jb, 04.40.+c
