Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
374 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. #10590311 | C2 | semidirect |
| 5. C3×#4481 | C2 | semidirect |
| 6. C3×#4479 | C2 | semidirect |
| 7. #10589096 | C2 | semidirect |
| 38. #4481 | D3 | semidirect |
| 39. #4479 | D3 | semidirect |
| 292. C32 | #1675 | semidirect |
| 336. C3 | #68497 | semidirect |
| 337. C3 | #68579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592541 | 2 |
| #10590327 | 2 |
| #10590311 | 2 |
| #10590300 | 2 |
| C3×#4481 | 2 |
| C3×#4479 | 2 |
| #10589096 | 2 |
| #68579 | 3 |
| #68497 | 3 |