Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
580 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 580 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×#88639 | C2 | semidirect |
| 2. #11721838 | C2 | semidirect |
| 3. C2×C9×#213 | C2 | semidirect |
| 4. C2×C3×#3672 | C2 | semidirect |
| 5. #11720295 | C2 | semidirect |
| 6. #11720282 | C2 | semidirect |
| 7. #11720276 | C2 | semidirect |
| 36. C2×#3672 | D3 | semidirect |
| 53. C9×D12 | D4 | semidirect |
| 55. C3×Dic18 | D4 | semidirect |
| 120. C2×#213 | D9 | semidirect |
| 174. Dic18 | #67 | semidirect |
| 267. C3×C9 | #449 | semidirect |
| 304. D12 | #611 | semidirect |
| 393. C9 | #5172 | semidirect |
| 447. C3 | #10588838 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88639 | 2 |
| #11721838 | 2 |
| C2×C9×#213 | 2 |
| C2×C3×#3672 | 2 |
| #11720295 | 2 |
| #11720282 | 2 |
| #11720276 | 2 |
| #10591520 | 3 |
| #10588838 | 3 |