Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
494 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#88548 | C2 | semidirect |
| 2. C3×#63506 | C2 | semidirect |
| 3. C2×C9×#215 | C2 | semidirect |
| 5. C2×#88423 | C2 | semidirect |
| 6. C2×#88416 | C2 | semidirect |
| 7. C3⋊C8×Dic9 | C2 | semidirect |
| 31. #63506 | D3 | semidirect |
| 53. C3⋊(C9⋊C8) | D4 | semidirect |
| 54. C9×C3⋊C8 | D4 | semidirect |
| 96. C3×Dic9 | SD16 | semidirect |
| 105. C2×#215 | D9 | semidirect |
| 214. Dic9 | #215 | semidirect |
| 222. C3×C9 | #492 | semidirect |
| 264. C3⋊C8 | #611 | semidirect |
| 317. C9 | #5085 | semidirect |
| 357. C3 | #10588855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88548 | 2 |
| C3×#63506 | 2 |
| C2×C9×#215 | 2 |
| #11721040 | 2 |
| C2×#88423 | 2 |
| C2×#88416 | 2 |
| C3⋊C8×Dic9 | 2 |
| #10591618 | 3 |
| #10588855 | 3 |