Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1225 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 1225 conjugacy classes of subgroups — too many to draw. Only its 188 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. C2×#63809 | C2 | semidirect |
| 3. #10593971 | C2 | semidirect |
| 4. C4×C8×C3⋊D3 | C2 | semidirect |
| 5. C3×#4696 | C2 | semidirect |
| 6. #10590905 | C2 | semidirect |
| 7. #10590886 | C2 | semidirect |
| 8. #10590884 | C2 | semidirect |
| 9. #10590353 | C2 | semidirect |
| 41. #4696 | D3 | semidirect |
| 60. C8×C3⋊D3 | D4 | semidirect |
| 61. C8×C3⋊D3 | D4 | semidirect |
| 193. C3⋊Dic3 | #135 | semidirect |
| 309. C32 | #3147 | semidirect |
| 351. C3 | #81820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63810 | 2 |
| C2×#63809 | 2 |
| #10593971 | 2 |
| C4×C8×C3⋊D3 | 2 |
| C3×#4696 | 2 |
| #10590905 | 2 |
| #10590886 | 2 |
| #10590884 | 2 |
| #10590353 | 2 |
| #81820 | 3 |