Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
580 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 580 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. #11721819 | C2 | semidirect |
| 3. C2×#88426 | C2 | semidirect |
| 4. C2×#88422 | C2 | semidirect |
| 5. C3×#63389 | C2 | semidirect |
| 6. #11720298 | C2 | semidirect |
| 7. #11720295 | C2 | semidirect |
| 39. #63389 | D3 | semidirect |
| 54. C9×D12 | D4 | semidirect |
| 57. C9×Dic6 | D4 | semidirect |
| 113. C2×#235 | D9 | semidirect |
| 267. C3×C9 | #449 | semidirect |
| 310. D12 | #611 | semidirect |
| 313. Dic6 | #611 | semidirect |
| 393. C9 | #4734 | semidirect |
| 447. 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 |
| #11721819 | 2 |
| C2×#88426 | 2 |
| C2×#88422 | 2 |
| C3×#63389 | 2 |
| #11720298 | 2 |
| #11720295 | 2 |
| #10591163 | 3 |
| #10588919 | 3 |