Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
428 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 107 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. #11721706 | C2 | semidirect |
| 4. C3×C4⋊(C9⋊C8) | C2 | semidirect |
| 5. #11720269 | C2 | semidirect |
| 28. C4⋊(C9⋊C8) | D3 | semidirect |
| 72. C3×C4×C9 | SD16 | semidirect |
| 168. C4×C9 | #204 | semidirect |
| 178. C3×C9 | #461 | semidirect |
| 246. C3×C4 | #3672 | semidirect |
| 258. C9 | #4841 | semidirect |
| 289. C4 | #88424 | semidirect |
| 293. C3 | #10588695 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721706 | 2 |
| C4×C9×D12 | 2 |
| C2×#88424 | 2 |
| C3×C4⋊(C9⋊C8) | 2 |
| #11720269 | 2 |
| #10590365 | 3 |
| #10588695 | 3 |