Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
458 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 458 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×#88523 | C2 | semidirect |
| 2. C2×C9×D24 | C2 | semidirect |
| 3. #11721045 | C2 | semidirect |
| 4. C3×#63377 | C2 | semidirect |
| 5. #11720294 | C2 | semidirect |
| 27. #63377 | D3 | semidirect |
| 38. C3×C8×C9 | D4 | semidirect |
| 76. C2×D24 | D9 | semidirect |
| 113. C8×C9 | D12 | semidirect |
| 174. C3×C9 | #469 | semidirect |
| 201. C3×C8 | #611 | semidirect |
| 254. C9 | #4865 | semidirect |
| 266. C8 | #6195 | semidirect |
| 289. C3 | #10588839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88523 | 2 |
| C2×C9×D24 | 2 |
| #11721045 | 2 |
| C3×#63377 | 2 |
| #11720294 | 2 |
| #10590846 | 3 |
| #10588839 | 3 |