Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
434 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 89 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×#63449 | C2 | semidirect |
| 3. C2×#88423 | C2 | semidirect |
| 4. C2×#88416 | C2 | semidirect |
| 5. #11720528 | C2 | semidirect |
| 6. C9×#809 | C2 | semidirect |
| 7. Dic9⋊(C3⋊C8) | C2 | semidirect |
| 33. #63449 | D3 | semidirect |
| 50. C3×Dic18 | D4 | semidirect |
| 98. C3×Dic9 | SD16 | semidirect |
| 112. #809 | D9 | semidirect |
| 150. Dic18 | D12 | semidirect |
| 221. Dic9 | #215 | semidirect |
| 229. C3×C9 | #460 | semidirect |
| 332. C9 | #5027 | semidirect |
| 378. C3 | #10588442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63449 | 2 |
| #11721040 | 2 |
| C2×#88423 | 2 |
| C2×#88416 | 2 |
| #11720528 | 2 |
| C9×#809 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| #10590549 | 3 |
| #10588442 | 3 |