Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
466 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 466 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×#875 | C2 | semidirect |
| 3. C2×#88428 | C2 | semidirect |
| 4. C2×#88426 | C2 | semidirect |
| 5. C2×#88424 | C2 | semidirect |
| 7. C3×C4×C9⋊C8 | C2 | semidirect |
| 37. C4×C9⋊C8 | D3 | semidirect |
| 108. #875 | D9 | semidirect |
| 220. C3×C9 | #495 | semidirect |
| 314. C9 | #4696 | semidirect |
| 353. C3 | #10588740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721712 | 2 |
| C9×#875 | 2 |
| C2×#88428 | 2 |
| C2×#88426 | 2 |
| C2×#88424 | 2 |
| C2×#88422 | 2 |
| C3×C4×C9⋊C8 | 2 |
| #10590370 | 3 |
| #10588740 | 3 |