Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1225 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1225 conjugacy classes of subgroups — too many to draw. Only its 200 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 |
|---|---|---|
| 1. C2×#63810 | C2 | semidirect |
| 2. #10593907 | C2 | semidirect |
| 3. C4×C8×C3⋊D3 | C2 | semidirect |
| 4. C3×#4699 | C2 | semidirect |
| 5. C3×#4695 | C2 | semidirect |
| 6. #10590869 | C2 | semidirect |
| 7. #10590375 | C2 | semidirect |
| 35. #4699 | D3 | semidirect |
| 36. #4695 | D3 | semidirect |
| 53. C8×C3⋊D3 | D4 | semidirect |
| 169. C32×C4 | #135 | semidirect |
| 269. C3×C4 | #912 | semidirect |
| 270. C3×C4 | #919 | semidirect |
| 280. C32 | #3147 | semidirect |
| 316. C4 | #63810 | semidirect |
| 319. C3 | #81782 | semidirect |
| 320. C3 | #81799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63810 | 2 |
| #10593907 | 2 |
| C4×C8×C3⋊D3 | 2 |
| C3×#4699 | 2 |
| C3×#4695 | 2 |
| #10590869 | 2 |
| #10590375 | 2 |
| #81799 | 3 |
| #81782 | 3 |