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. C22×Dic33 | C2 | semidirect |
| 2. C2×C11×#67 | C2 | semidirect |
| 3. C2×C3×C22⋊D11 | C2 | semidirect |
| 4. C2×#63143 | C2 | semidirect |
| 5. C2×#63140 | C2 | semidirect |
| 6. C2×D3×Dic11 | C2 | semidirect |
| 7. #10587242 | C2 | direct (N × H) |
| 8. C2×Dic3×D11 | C2 | semidirect |
| 15. C2×Dic33 | C22 | semidirect |
| 16. C11×#67 | C22 | semidirect |
| 18. C3×C22⋊D11 | C22 | semidirect |
| 20. #63143 | C22 | semidirect |
| 21. #63140 | C22 | semidirect |
| 22. D3×Dic11 | C22 | semidirect |
| 23. Dic3×D11 | C22 | semidirect |
| 26. C2×C22⋊D11 | D3 | semidirect |
| 50. C22⋊D11 | C2×D3 | semidirect |
| 59. C2×C3×C11 | #41 | semidirect |
| 65. C2×#67 | D11 | semidirect |
| 82. C3×C11 | C2×#41 | semidirect |
| 90. #67 | C2×D11 | semidirect |
| 100. C2×C11 | #237 | semidirect |
| 122. C11 | C2×#237 | semidirect |
| 139. C2×C3 | #4341 | semidirect |
| 153. C3 | C2×#4341 | semidirect |
| 157. C2 | #10587242 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic33 | 2 |
| C2×C11×#67 | 2 |
| C2×C3×C22⋊D11 | 2 |
| C2×#63143 | 2 |
| C2×#63140 | 2 |
| C2×D3×Dic11 | 2 |
| #10587242 | 2 |
| C2×Dic3×D11 | 2 |
| C2×#4341 | 3 |
| C2×#237 | 11 |