Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
508 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 508 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. #11721712 | C2 | semidirect |
| 2. C9×#874 | C2 | semidirect |
| 3. C2×#88424 | C2 | semidirect |
| 4. C2×#88422 | C2 | semidirect |
| 5. C3×#63362 | C2 | semidirect |
| 27. #63362 | D3 | semidirect |
| 38. C3×C9⋊C8 | D4 | semidirect |
| 79. #874 | D9 | semidirect |
| 109. C9⋊C8 | D12 | semidirect |
| 164. C3×C9 | #496 | semidirect |
| 237. C9 | #4712 | semidirect |
| 269. C3 | #10588756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721712 | 2 |
| C9×#874 | 2 |
| C2×#88424 | 2 |
| C2×#88422 | 2 |
| C3×#63362 | 2 |
| #10590371 | 3 |
| #10588756 | 3 |