Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
594 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 594 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 |
|---|---|---|
| 1. #11721711 | C2 | semidirect |
| 2. C9×#874 | C2 | semidirect |
| 3. C2×#88422 | C2 | semidirect |
| 4. C3×C4×C9⋊C8 | C2 | semidirect |
| 22. C4×C9⋊C8 | D3 | semidirect |
| 31. C3×C9⋊C8 | D4 | semidirect |
| 56. C3×C4×C9 | D8 | semidirect |
| 64. #874 | D9 | semidirect |
| 89. C9⋊C8 | D12 | semidirect |
| 129. C4×C9 | D24 | semidirect |
| 135. C3×C9 | #493 | semidirect |
| 192. C3×C4 | #3673 | semidirect |
| 198. C9 | #4695 | semidirect |
| 224. C4 | #88422 | semidirect |
| 227. C3 | #10588755 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721711 | 2 |
| C9×#874 | 2 |
| C2×#88422 | 2 |
| C3×C4×C9⋊C8 | 2 |
| #10590350 | 3 |
| #10588755 | 3 |