Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
458 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 87 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×D24 | C2 | semidirect |
| 2. #11721043 | C2 | semidirect |
| 3. #11721025 | C2 | semidirect |
| 4. C2×#88421 | C2 | semidirect |
| 5. #11720537 | C2 | semidirect |
| 6. C3×#63380 | C2 | semidirect |
| 7. #11720294 | C2 | semidirect |
| 35. #63380 | D3 | semidirect |
| 48. C9×D12 | D4 | semidirect |
| 100. C3⋊Dic9 | D8 | semidirect |
| 108. C2×D24 | D9 | semidirect |
| 236. C3×C9 | #459 | semidirect |
| 270. D12 | #611 | semidirect |
| 343. C9 | #4786 | semidirect |
| 393. C3 | #10588830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D24 | 2 |
| #11721043 | 2 |
| #11721025 | 2 |
| C2×#88421 | 2 |
| #11720537 | 2 |
| C3×#63380 | 2 |
| #11720294 | 2 |
| #10590749 | 3 |
| #10588830 | 3 |