Abstract. We study a subgroup F r(162 × 4) of SU (3) of order 648 which is an extension of D(9, 1, 1; 2, 1, 1) and whose generators arise from anyonic systems. We show that this group is isomorphic to a semi-direct product (Z/18Z×Z/6Z) S 3 with respect to conjugation and we give a presentation of the group. We show that the group D(18, 1, 1; 2, 1, 1) from the series (D) in the existing classification for finite SU (3)-subgroups is also isomorphic to a semi-direct product (Z/18Z × Z/6Z) S 3 , also with respect to conjugation. We show that the two groups F r(162×4) and D(18, 1, 1; 2, 1, 1) are isomorphic and we provide an isomorphism between both groups. We prove that F r(162 × 4) is not isomorphic to the exceptional SU (3) subgroup Σ(216×3) of the same order 648. We further prove that the only SU (3) finite subgroups from the 1916 classification by Blichfeldt or its extended version which F r(162 × 4) may be isomorphic to belong to the (D)-series. Finally, we show that F r(162 × 4) and D(18, 1, 1; 2, 1, 1) are both conjugate under an orthogonal matrix which we provide.