Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
| 4. C9×#819 | C2 | semidirect |
| 5. #11720289 | C2 | semidirect |
| 27. C2×Dic36 | D3 | semidirect |
| 87. #819 | D9 | semidirect |
| 173. C3×C9 | #473 | semidirect |
| 245. C9 | #5192 | semidirect |
| 274. C3 | #10588576 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721770 | 2 |
| C2×C3×Dic36 | 2 |
| #11720871 | 2 |
| C9×#819 | 2 |
| #11720289 | 2 |
| #10590933 | 3 |
| #10588576 | 3 |