Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
668 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 668 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×#5076 | C2 | semidirect |
| 3. #10590300 | C2 | semidirect |
| 4. #10590284 | C2 | semidirect |
| 5. C3×#4544 | C2 | semidirect |
| 6. #10589085 | C2 | semidirect |
| 7. #10589082 | C2 | semidirect |
| 33. #5076 | D3 | semidirect |
| 37. #4544 | D3 | semidirect |
| 131. #634 | SD16 | semidirect |
| 398. C32 | #1631 | semidirect |
| 458. C3 | #68405 | semidirect |
| 459. C3 | #71271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596189 | 2 |
| C3×#5076 | 2 |
| #10590300 | 2 |
| #10590284 | 2 |
| C3×#4544 | 2 |
| #10589085 | 2 |
| #10589082 | 2 |
| #71271 | 3 |
| #68405 | 3 |