Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
575 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 575 conjugacy classes of subgroups — too many to draw. Only its 102 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×#4707 | C2 | semidirect |
| 3. #10590334 | C2 | semidirect |
| 4. #10589330 | C2 | semidirect |
| 5. C3×#4464 | C2 | semidirect |
| 6. #10589087 | C2 | semidirect |
| 7. #10589086 | C2 | semidirect |
| 34. #4707 | D3 | semidirect |
| 43. #4464 | D3 | semidirect |
| 404. C32 | #1525 | semidirect |
| 468. C3 | #68342 | semidirect |
| 469. C3 | #69859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593969 | 2 |
| C3×#4707 | 2 |
| #10590334 | 2 |
| #10589330 | 2 |
| C3×#4464 | 2 |
| #10589087 | 2 |
| #10589086 | 2 |
| #69859 | 3 |
| #68342 | 3 |