Finite Group DatabasebetaFinite Group DatabasebetaOrder 1056.
312 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 122 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. Q8×D33 | C2 | semidirect |
| 2. D3×Q8×C11 | C2 | semidirect |
| 3. C3×Q8×D11 | C2 | semidirect |
| 5. D33⋊Q8 | C2 | semidirect |
| 6. D3×Dic22 | C2 | semidirect |
| 7. D11×Dic6 | C2 | semidirect |
| 10. C3×Q8×C11 | C22 | semidirect |
| 12. Dic66 | C22 | semidirect |
| 14. C11×Dic6 | C22 | semidirect |
| 16. C3×Dic22 | C22 | semidirect |
| 17. #63143 | C22 | semidirect |
| 25. Q8×D11 | D3 | direct (N × H) |
| 31. D3×D11 | Q8 | direct (N × H) |
| 39. Q8×C11 | C2×D3 | semidirect |
| 48. Dic22 | C2×D3 | semidirect |
| 50. D33 | C2×Q8 | semidirect |
| 51. C3×D11 | C2×Q8 | semidirect |
| 52. D3×C11 | C2×Q8 | semidirect |
| 57. D3×Q8 | D11 | direct (N × H) |
| 68. C3×C11 | C22×Q8 | semidirect |
| 72. C3×Q8 | C2×D11 | semidirect |
| 81. Dic6 | C2×D11 | semidirect |
| 85. D11 | D3×Q8 | direct (N × H) |
| 101. C11 | C2×D3×Q8 | semidirect |
| 107. Q8 | D3×D11 | direct (N × H) |
| 117. D3 | Q8×D11 | direct (N × H) |
| 126. C3 | C2×Q8×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D33 | 2 |
| D3×Q8×C11 | 2 |
| C3×Q8×D11 | 2 |
| C4×D3×D11 | 2 |
| D33⋊Q8 | 2 |
| D3×Dic22 | 2 |
| D11×Dic6 | 2 |
| C2×Q8×D11 | 3 |
| C2×D3×Q8 | 11 |