Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
470 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 91 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. #11721040 | C2 | semidirect |
| 3. D12×Dic9 | C2 | semidirect |
| 4. C2×#88422 | C2 | semidirect |
| 5. #11720543 | C2 | semidirect |
| 6. C3×Dic9⋊C8 | C2 | semidirect |
| 7. #11720295 | C2 | semidirect |
| 37. Dic9⋊C8 | D3 | semidirect |
| 50. C9×D12 | D4 | semidirect |
| 101. C3×Dic9 | D8 | semidirect |
| 107. C2×D24 | D9 | semidirect |
| 231. Dic9 | D24 | semidirect |
| 239. C3×C9 | #459 | semidirect |
| 275. D12 | #611 | semidirect |
| 350. C9 | #4843 | semidirect |
| 401. 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 |
| #11721040 | 2 |
| D12×Dic9 | 2 |
| C2×#88422 | 2 |
| #11720543 | 2 |
| C3×Dic9⋊C8 | 2 |
| #11720295 | 2 |
| #10590753 | 3 |
| #10588830 | 3 |