Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
338 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11720927 | C2 | semidirect |
| 4. C8×C9×Dic3 | C2 | semidirect |
| 5. C3×#63376 | C2 | semidirect |
| 7. #11720276 | C2 | semidirect |
| 35. #63376 | D3 | semidirect |
| 100. C8×Dic3 | D9 | semidirect |
| 200. C3×C9 | #488 | semidirect |
| 287. C9 | #4800 | semidirect |
| 325. C3 | #10588379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720952 | 2 |
| #11720927 | 2 |
| #11720543 | 2 |
| C8×C9×Dic3 | 2 |
| C3×#63376 | 2 |
| #11720284 | 2 |
| #11720276 | 2 |
| #10590872 | 3 |
| #10588379 | 3 |