Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
408 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 105 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. #11720912 | C2 | semidirect |
| 4. #11720527 | C2 | semidirect |
| 5. C3×#63367 | C2 | semidirect |
| 7. Dic3×C9⋊C8 | C2 | semidirect |
| 21. #88424 | C4 | semidirect |
| 35. #63367 | D3 | semidirect |
| 42. #6226 | C2×C4 | semidirect |
| 50. C3×C9⋊C8 | C2×C4 | semidirect |
| 89. C9×Dic3 | SD16 | semidirect |
| 139. C9⋊C8 | C4×D3 | semidirect |
| 206. C3×C9 | C4×SD16 | semidirect |
| 290. Dic3 | #3672 | semidirect |
| 293. C9 | #4852 | semidirect |
| 331. C3 | C4×#3672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#893 | 2 |
| #11720912 | 2 |
| C2×#88424 | 2 |
| #11720527 | 2 |
| C3×#63367 | 2 |
| #11720294 | 2 |
| Dic3×C9⋊C8 | 2 |
| #10590479 | 3 |
| C4×#3672 | 3 |