Finite Group DatabasebetaFinite Group DatabasebetaOrder 1056.
156 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 2. C22×Dic33 | C2 | semidirect |
| 3. C3×C11×C22⋊C4 | C2 | semidirect |
| 4. #10587203 | C2 | semidirect |
| 5. C4⋊Dic33 | C2 | semidirect |
| 16. C11×C22⋊C4 | D3 | semidirect |
| 41. C3×C22⋊C4 | D11 | semidirect |
| 52. C3×C11 | #123 | semidirect |
| 69. C22⋊C4 | D33 | semidirect |
| 78. C11 | #886 | semidirect |
| 98. C3 | #66939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63159 | 2 |
| C22×Dic33 | 2 |
| C3×C11×C22⋊C4 | 2 |
| #10587203 | 2 |
| C4⋊Dic33 | 2 |
| #66939 | 3 |
| #886 | 11 |