Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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. Dic6×Dic9 | C2 | semidirect |
| 5. #11720297 | C2 | semidirect |
| 6. #11720278 | C2 | semidirect |
| 7. C3⋊C8×Dic9 | C2 | semidirect |
| 16. C9×#214 | C4 | semidirect |
| 48. C9×Dic6 | C2×C4 | semidirect |
| 50. C9×C3⋊C8 | C2×C4 | semidirect |
| 90. C3×Dic9 | SD16 | semidirect |
| 158. #214 | Dic9 | direct (N × H) |
| 200. Dic9 | #214 | direct (N × H) |
| 208. C3×C9 | C4×SD16 | semidirect |
| 237. Dic6 | C2×Dic9 | semidirect |
| 242. C3⋊C8 | C2×Dic9 | semidirect |
| 298. C9 | C4×#214 | semidirect |
| 337. C3 | SD16×Dic9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×Dic9 | 2 |
| C2×C9×#214 | 2 |
| Dic6×Dic9 | 2 |
| #11720576 | 2 |
| #11720297 | 2 |
| #11720278 | 2 |
| C3⋊C8×Dic9 | 2 |
| Dic3×#214 | 3 |
| SD16×Dic9 | 3 |