Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
536 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. C2×C9×#235 | C2 | semidirect |
| 2. C3×#63492 | C2 | semidirect |
| 3. C2×#88425 | C2 | semidirect |
| 4. C2×#88421 | C2 | semidirect |
| 5. #11720571 | C2 | semidirect |
| 6. #11720297 | C2 | semidirect |
| 7. #11720294 | C2 | semidirect |
| 35. #63492 | D3 | semidirect |
| 52. C9×D12 | D4 | semidirect |
| 57. C9×Dic6 | D4 | semidirect |
| 111. C2×#235 | D9 | semidirect |
| 256. C3×C9 | #449 | semidirect |
| 294. D12 | #611 | semidirect |
| 297. Dic6 | #611 | semidirect |
| 374. C9 | #5037 | semidirect |
| 427. C3 | #10588919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#235 | 2 |
| C3×#63492 | 2 |
| C2×#88425 | 2 |
| C2×#88421 | 2 |
| #11720571 | 2 |
| #11720297 | 2 |
| #11720294 | 2 |
| #10591161 | 3 |
| #10588919 | 3 |