Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
554 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 89 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×#88641 | C2 | semidirect |
| 2. C2×#88524 | C2 | semidirect |
| 3. #11721038 | C2 | semidirect |
| 4. C2×#88417 | C2 | semidirect |
| 5. C9×(C2×D3)⋊C8 | C2 | semidirect |
| 6. C3×#63380 | C2 | semidirect |
| 7. #11720277 | C2 | semidirect |
| 38. #63380 | D3 | semidirect |
| 48. #6226 | D4 | semidirect |
| 54. C3×D36 | D4 | semidirect |
| 123. (C2×D3)⋊C8 | D9 | semidirect |
| 165. D36 | D12 | semidirect |
| 259. C3×C9 | #449 | semidirect |
| 378. C9 | #4781 | semidirect |
| 431. C3 | #10588416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88641 | 2 |
| C2×#88524 | 2 |
| #11721038 | 2 |
| C2×#88417 | 2 |
| C9×(C2×D3)⋊C8 | 2 |
| C3×#63380 | 2 |
| #11720277 | 2 |
| #10590968 | 3 |
| #10588416 | 3 |