Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
494 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 101 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. C9×#944 | C2 | semidirect |
| 3. C2×C3×#3675 | C2 | semidirect |
| 5. C2×#88426 | C2 | semidirect |
| 6. C2×#88425 | C2 | semidirect |
| 7. Dic3×C9⋊C8 | C2 | semidirect |
| 35. C2×#3675 | D3 | semidirect |
| 53. C3⋊(C9⋊C8) | D4 | semidirect |
| 54. C3×C9⋊C8 | D4 | semidirect |
| 96. C9×Dic3 | SD16 | semidirect |
| 99. #944 | D9 | semidirect |
| 153. C9⋊C8 | #67 | semidirect |
| 222. C3×C9 | #492 | semidirect |
| 314. Dic3 | #3675 | semidirect |
| 317. C9 | #5175 | semidirect |
| 357. C3 | #10588770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88548 | 2 |
| C9×#944 | 2 |
| C2×C3×#3675 | 2 |
| #11721006 | 2 |
| C2×#88426 | 2 |
| C2×#88425 | 2 |
| Dic3×C9⋊C8 | 2 |
| #10591618 | 3 |
| #10588770 | 3 |