  Let $G$ be a finitely generate nilpotent class-2 torsion-free group. We study
how the zeta function enumerating normal subgroups of G varies on residue
classes. In particular, we show that for small such $G$ of Hirsch length less
than or equal to 7, the normal zeta functions are generically always rational
functions on residue classes. We then show that there are examples of groups
with Hirsch length 8 whose normal zeta function is not a rational function on
residue classes. We observe the connection to Higman's PORC conjecture.
