  The subgroup zeta function and the normal zeta function of a finitely
generated virtually nilpotent group can be expressed as finite sums of
Dirichlet series admitting Euler product factorization. We compute these series
except for a finite number of local factors when the group is virtually
nilpotent of Hirsch length 3. We deduce that they can be meromorphically
continued to the whole complex plane and that they satisfy local functional
equations. The complete computation (with no exception of local factors) is
presented for those groups that are also torsion-free, that is, for the
3-dimensional almost-Bieberbach groups.
