Finite Group DatabasebetaFinite Group DatabasebetaOrder 1056.
184 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 3. C4⋊Dic33 | C2 | semidirect |
| 4. C11×C4⋊Dic3 | C2 | semidirect |
| 5. Dic11⋊Dic3 | C2 | semidirect |
| 12. C3×C4×D11 | C4 | semidirect |
| 23. C3×C4×C11 | C2×C4 | semidirect |
| 25. C3×Dic11 | C2×C4 | semidirect |
| 34. C4×D11 | Dic3 | semidirect |
| 38. C3×D11 | C4⋊C4 | semidirect |
| 43. C4⋊Dic3 | D11 | direct (N × H) |
| 49. C4×C11 | C2×Dic3 | semidirect |
| 51. Dic11 | C2×Dic3 | semidirect |
| 52. C3×C11 | C2×C4⋊C4 | semidirect |
| 64. D11 | C4⋊Dic3 | direct (N × H) |
| 75. C3×C4 | C4×D11 | semidirect |
| 78. C11 | C2×C4⋊Dic3 | semidirect |
| 97. C4 | Dic3×D11 | semidirect |
| 98. C3 | C4⋊C4×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D11 | 2 |
| C2×Dic3×D11 | 2 |
| C4⋊Dic33 | 2 |
| C11×C4⋊Dic3 | 2 |
| Dic11⋊Dic3 | 2 |
| C4⋊C4×D11 | 3 |
| C2×C4⋊Dic3 | 11 |