Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
436 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #11721025 | C2 | semidirect |
| 3. #11720538 | C2 | semidirect |
| 4. C3×#63377 | C2 | semidirect |
| 5. #11720294 | C2 | semidirect |
| 14. C9×D24 | C4 | semidirect |
| 24. #63377 | D3 | semidirect |
| 32. C9×D12 | C2×C4 | semidirect |
| 34. C3×C8×C9 | C2×C4 | semidirect |
| 95. C8×C9 | C4×D3 | semidirect |
| 120. D24 | Dic9 | semidirect |
| 146. C3×C9 | #442 | semidirect |
| 161. D12 | C2×Dic9 | semidirect |
| 164. C3×C8 | C2×Dic9 | semidirect |
| 207. C9 | #4869 | semidirect |
| 216. C8 | D3×Dic9 | semidirect |
| 234. C3 | #10588832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D24 | 2 |
| #11721025 | 2 |
| #11720538 | 2 |
| C3×#63377 | 2 |
| #11720294 | 2 |
| #10590781 | 3 |
| #10588832 | 3 |