Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
554 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 554 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×#239 | C2 | semidirect |
| 2. C2×#88548 | C2 | semidirect |
| 3. #11721038 | C2 | semidirect |
| 4. C2×#88422 | C2 | semidirect |
| 5. C3×#63395 | C2 | semidirect |
| 6. #11720294 | C2 | semidirect |
| 7. (C2×D3)⋊(C9⋊C8) | C2 | semidirect |
| 37. #63395 | D3 | semidirect |
| 44. C3×Q8×C9 | D4 | semidirect |
| 53. C9×D12 | D4 | semidirect |
| 112. C2×#239 | D9 | semidirect |
| 153. Q8×C9 | D12 | semidirect |
| 259. C3×C9 | #449 | semidirect |
| 271. C3×Q8 | #611 | semidirect |
| 299. D12 | #611 | semidirect |
| 378. C9 | #4810 | semidirect |
| 383. Q8 | #6195 | semidirect |
| 431. C3 | #10588919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#239 | 2 |
| C2×#88548 | 2 |
| #11721038 | 2 |
| C2×#88422 | 2 |
| C3×#63395 | 2 |
| #11720294 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #10591588 | 3 |
| #10588919 | 3 |