Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
350 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11720969 | C2 | semidirect |
| 4. C9×#816 | C2 | semidirect |
| 5. C3×#63375 | C2 | semidirect |
| 6. #11720298 | C2 | semidirect |
| 34. #63375 | D3 | semidirect |
| 100. #816 | D9 | semidirect |
| 203. C3×C9 | #489 | semidirect |
| 292. C9 | #4714 | semidirect |
| 331. C3 | #10588474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720969 | 2 |
| #11720953 | 2 |
| #11720543 | 2 |
| C9×#816 | 2 |
| C3×#63375 | 2 |
| #11720298 | 2 |
| #11720267 | 2 |
| #10590893 | 3 |
| #10588474 | 3 |