Enumeration conjecture for symmetry-group orders of two-step rules

Let $\mathcal Q$ be the class of two-step rules, and let $\mathcal N_\ell$ denote the set of rules in $\mathcal Q$ whose symmetry group has order $\ell$, with $\ell=\infty$ allowed. Symmetry-group enumeration conjecture.

$$|\mathcal N_4|=1084,\qquad |\mathcal N_6|=443,\qquad |\mathcal N_8|=146,$$ $$|\mathcal N_{10}|=66,\qquad |\mathcal N_{12}|=6,\qquad |\mathcal N_\infty|=5164.$$

These values come from the paper's computational classification of 6909 non-trivial quarter-plane models; the supplied source gives no resolution, so the conjecture remains open.