Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
521 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 521 conjugacy classes of subgroups — too many to draw. Only its 90 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. C3×#4846 | C2 | semidirect |
| 3. #10590379 | C2 | semidirect |
| 4. #10590309 | C2 | semidirect |
| 5. #10589349 | C2 | semidirect |
| 6. C3×#4482 | C2 | semidirect |
| 7. #10589080 | C2 | semidirect |
| 33. #4846 | D3 | semidirect |
| 41. #4482 | D3 | semidirect |
| 119. C3×D12 | SD16 | semidirect |
| 269. D12 | #215 | semidirect |
| 363. C32 | #1654 | semidirect |
| 421. C3 | #68439 | semidirect |
| 422. C3 | #71111 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593896 | 2 |
| C3×#4846 | 2 |
| #10590379 | 2 |
| #10590309 | 2 |
| #10589349 | 2 |
| C3×#4482 | 2 |
| #10589080 | 2 |
| #71111 | 3 |
| #68439 | 3 |