Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
416 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. Dic3×Dic18 | C2 | semidirect |
| 5. #11720268 | C2 | semidirect |
| 6. #11720264 | C2 | semidirect |
| 7. Dic3×C9⋊C8 | C2 | semidirect |
| 16. C3×#3672 | C4 | semidirect |
| 48. C3×Dic18 | C2×C4 | semidirect |
| 50. C3×C9⋊C8 | C2×C4 | semidirect |
| 72. #3672 | Dic3 | direct (N × H) |
| 89. C9×Dic3 | SD16 | semidirect |
| 136. Dic18 | C2×Dic3 | semidirect |
| 139. C9⋊C8 | C2×Dic3 | semidirect |
| 208. C3×C9 | C4×SD16 | semidirect |
| 295. Dic3 | #3672 | direct (N × H) |
| 298. C9 | Dic3×SD16 | semidirect |
| 337. C3 | C4×#3672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C9×Dic3 | 2 |
| C2×C3×#3672 | 2 |
| Dic3×Dic18 | 2 |
| #11720576 | 2 |
| #11720268 | 2 |
| #11720264 | 2 |
| Dic3×C9⋊C8 | 2 |
| Dic3×#214 | 3 |
| C4×#3672 | 3 |