Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
348 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 85 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. C3×#63469 | C2 | semidirect |
| 3. #11720877 | C2 | semidirect |
| 4. #11720555 | C2 | semidirect |
| 5. C9×#825 | C2 | semidirect |
| 6. #11720260 | C2 | semidirect |
| 7. Dic3×C9⋊C8 | C2 | semidirect |
| 19. #88427 | C4 | semidirect |
| 20. #88425 | C4 | semidirect |
| 21. #88423 | C4 | semidirect |
| 22. #88421 | C4 | semidirect |
| 34. #63469 | D3 | semidirect |
| 107. #825 | D9 | semidirect |
| 215. C3×C9 | #443 | semidirect |
| 299. C9 | #5144 | semidirect |
| 335. C3 | #10588504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63469 | 2 |
| #11720881 | 2 |
| #11720877 | 2 |
| #11720555 | 2 |
| C9×#825 | 2 |
| #11720260 | 2 |
| Dic3×C9⋊C8 | 2 |
| #10590975 | 3 |
| #10588504 | 3 |