Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
534 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C9×#869 | C2 | semidirect |
| 3. C2×#88426 | C2 | semidirect |
| 4. C3×C4×C9⋊C8 | C2 | semidirect |
| 22. C4×C9⋊C8 | D3 | semidirect |
| 30. C3×C9⋊C8 | D4 | semidirect |
| 53. C3×C4×C9 | SD16 | semidirect |
| 62. #869 | D9 | semidirect |
| 85. C9⋊C8 | D12 | semidirect |
| 122. C4×C9 | #204 | semidirect |
| 128. C3×C9 | #492 | semidirect |
| 178. C3×C4 | #3675 | semidirect |
| 185. C9 | #4693 | semidirect |
| 207. C4 | #88426 | semidirect |
| 210. C3 | #10588770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721711 | 2 |
| C9×#869 | 2 |
| C2×#88426 | 2 |
| C3×C4×C9⋊C8 | 2 |
| #10590373 | 3 |
| #10588770 | 3 |