Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
729 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 729 conjugacy classes of subgroups — too many to draw. Only its 150 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. C22×C3×Dic12 | C2 | semidirect |
| 3. C2×C3×#824 | C2 | semidirect |
| 5. C32×#341 | C2 | semidirect |
| 7. #68944 | C3 | direct (N × H) |
| 24. C22×Dic12 | C2×C3 | semidirect |
| 27. C2×#824 | C2×C3 | semidirect |
| 30. C3×#341 | D3 | semidirect |
| 31. C3×#341 | C2×C3 | semidirect |
| 111. #341 | C3×D3 | semidirect |
| 294. C32 | #2020 | semidirect |
| 339. C3 | #68944 | direct (N × H) |
| 340. C3 | C3×#2020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#909 | 2 |
| C22×C3×Dic12 | 2 |
| C2×C3×#824 | 2 |
| C3×#5110 | 2 |
| C32×#341 | 2 |
| C3×#2020 | 3 |
| #68944 | 3 |