Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
508 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 508 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. #11721712 | C2 | semidirect |
| 2. C3×#63436 | C2 | semidirect |
| 3. C2×#88417 | C2 | semidirect |
| 4. C2×#88415 | C2 | semidirect |
| 5. C9×#803 | C2 | semidirect |
| 26. #63436 | D3 | semidirect |
| 38. C9×C3⋊C8 | D4 | semidirect |
| 81. #803 | D9 | semidirect |
| 164. C3×C9 | #496 | semidirect |
| 192. C3⋊C8 | D36 | semidirect |
| 237. C9 | #5074 | semidirect |
| 269. C3 | #10588393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721712 | 2 |
| C3×#63436 | 2 |
| C2×#88417 | 2 |
| C2×#88415 | 2 |
| C9×#803 | 2 |
| #10590371 | 3 |
| #10588393 | 3 |