Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
452 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 87 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×#88543 | C2 | semidirect |
| 3. #11720913 | C2 | semidirect |
| 4. C2×#88415 | C2 | semidirect |
| 5. C9×#832 | C2 | semidirect |
| 6. Dic9⋊(C3⋊C8) | C2 | semidirect |
| 7. #11720266 | C2 | semidirect |
| 45. #6226 | D4 | semidirect |
| 99. C3×Dic9 | SD16 | semidirect |
| 111. #832 | D9 | semidirect |
| 225. Dic9 | #214 | semidirect |
| 233. C3×C9 | #460 | semidirect |
| 338. C9 | #5075 | semidirect |
| 384. C3 | #10588442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88543 | 2 |
| C3×#63502 | 2 |
| #11720913 | 2 |
| C2×#88415 | 2 |
| C9×#832 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| #11720266 | 2 |
| #10591439 | 3 |
| #10588442 | 3 |