Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
466 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×C3×Dic36 | C2 | semidirect |
| 3. #11720952 | C2 | semidirect |
| 4. C2×#88416 | C2 | semidirect |
| 5. C8×C9×Dic3 | C2 | semidirect |
| 25. C2×Dic36 | D3 | semidirect |
| 78. C8×Dic3 | D9 | semidirect |
| 153. C3×C9 | #495 | semidirect |
| 218. C9 | #5191 | semidirect |
| 246. C3 | #10588378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88525 | 2 |
| C2×C3×Dic36 | 2 |
| #11720952 | 2 |
| C2×#88416 | 2 |
| C8×C9×Dic3 | 2 |
| #10590865 | 3 |
| #10588378 | 3 |