Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
337 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 337 conjugacy classes of subgroups — too many to draw. Only its 80 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. C3×#4878 | C2 | semidirect |
| 3. #10589357 | C2 | semidirect |
| 4. C3×#4491 | C2 | semidirect |
| 5. #10589116 | C2 | semidirect |
| 6. #10589114 | C2 | semidirect |
| 7. #10589103 | C2 | semidirect |
| 23. #4878 | D3 | semidirect |
| 34. #4491 | D3 | semidirect |
| 264. C32 | #2244 | semidirect |
| 309. C3 | #69186 | semidirect |
| 310. C3 | #71352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4878 | 2 |
| #10590880 | 2 |
| #10589357 | 2 |
| C3×#4491 | 2 |
| #10589116 | 2 |
| #10589114 | 2 |
| #10589103 | 2 |
| #71352 | 3 |
| #69186 | 3 |