Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
272 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 57 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. #11720829 | C2 | semidirect |
| 3. #11720506 | C2 | semidirect |
| 4. C9×#800 | C2 | semidirect |
| 5. C3×Dic72 | C2 | semidirect |
| 6. #11720244 | C2 | semidirect |
| 7. #11720240 | C2 | semidirect |
| 33. Dic72 | D3 | semidirect |
| 92. #800 | D9 | semidirect |
| 174. C3×C9 | #510 | semidirect |
| 238. C9 | #4918 | semidirect |
| 266. C3 | #10588595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720829 | 2 |
| #11720824 | 2 |
| #11720506 | 2 |
| C9×#800 | 2 |
| C3×Dic72 | 2 |
| #11720244 | 2 |
| #11720240 | 2 |
| #10590246 | 3 |
| #10588595 | 3 |