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 |
|---|---|---|
| 2. #10590873 | C2 | semidirect |
| 3. #10589375 | C2 | semidirect |
| 4. C3×#4509 | C2 | semidirect |
| 5. C3×#4502 | C2 | semidirect |
| 6. #10589116 | C2 | semidirect |
| 7. #10589115 | C2 | semidirect |
| 33. #4509 | D3 | semidirect |
| 34. #4502 | D3 | semidirect |
| 264. C32 | #2244 | semidirect |
| 309. C3 | #69080 | semidirect |
| 310. C3 | #69186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590880 | 2 |
| #10590873 | 2 |
| #10589375 | 2 |
| C3×#4509 | 2 |
| C3×#4502 | 2 |
| #10589116 | 2 |
| #10589115 | 2 |
| #69186 | 3 |
| #69080 | 3 |