Finite Group DatabasebetaFinite Group DatabasebetaOrder 1056.
328 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 116 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×#63159 | C2 | semidirect |
| 2. C22×C11×Dic3 | C2 | semidirect |
| 3. C2×C3×C22⋊D11 | C2 | semidirect |
| 4. C2×#63143 | C2 | semidirect |
| 5. C2×#63141 | C2 | semidirect |
| 6. C2×D33⋊C4 | C2 | semidirect |
| 7. #10587241 | C2 | direct (N × H) |
| 8. C2×Dic3×D11 | C2 | semidirect |
| 13. #63159 | C22 | semidirect |
| 17. C2×C11×Dic3 | C22 | semidirect |
| 18. C3×C22⋊D11 | C22 | semidirect |
| 20. #63143 | C22 | semidirect |
| 21. #63141 | C22 | semidirect |
| 22. D33⋊C4 | C22 | semidirect |
| 23. Dic3×D11 | C22 | semidirect |
| 26. C2×C22⋊D11 | D3 | semidirect |
| 51. C22⋊D11 | C2×D3 | semidirect |
| 59. C2×C3×C11 | #41 | semidirect |
| 67. C22×Dic3 | D11 | semidirect |
| 82. C3×C11 | C2×#41 | semidirect |
| 95. C2×Dic3 | C2×D11 | semidirect |
| 99. C2×C11 | #237 | semidirect |
| 122. C11 | C2×#237 | semidirect |
| 139. C2×C3 | #4339 | semidirect |
| 153. C3 | C2×#4339 | semidirect |
| 157. C2 | #10587241 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63159 | 2 |
| C22×C11×Dic3 | 2 |
| C2×C3×C22⋊D11 | 2 |
| C2×#63143 | 2 |
| C2×#63141 | 2 |
| C2×D33⋊C4 | 2 |
| #10587241 | 2 |
| C2×Dic3×D11 | 2 |
| C2×#4339 | 3 |
| C2×#237 | 11 |