Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
387 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 387 conjugacy classes of subgroups — too many to draw. Only its 96 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×#4682 | C2 | semidirect |
| 4. C3×#4458 | C2 | semidirect |
| 5. #10589095 | C2 | semidirect |
| 25. #4682 | D3 | semidirect |
| 29. #4458 | D3 | semidirect |
| 239. C32 | #1675 | semidirect |
| 279. C3 | #68579 | semidirect |
| 280. C3 | #71372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C4⋊(C3⋊D3) | 2 |
| C3×#4682 | 2 |
| #10590300 | 2 |
| C3×#4458 | 2 |
| #10589095 | 2 |
| #71372 | 3 |
| #68579 | 3 |