Finite Group DatabasebetaFinite Group DatabasebetaOrder 1056.
188 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 65 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. C2×C4×D33 | C2 | semidirect |
| 4. C3×C11×C22⋊C4 | C2 | semidirect |
| 5. #10587203 | C2 | semidirect |
| 6. #10587201 | C2 | semidirect |
| 7. C4×Dic33 | C2 | semidirect |
| 13. #63159 | C4 | semidirect |
| 22. C11×C22⋊C4 | D3 | semidirect |
| 28. C22×C3×C11 | C2×C4 | semidirect |
| 32. C2×D33 | C2×C4 | semidirect |
| 36. Dic33 | C2×C4 | semidirect |
| 37. Dic33 | D4 | semidirect |
| 57. C3×C22⋊C4 | D11 | semidirect |
| 63. C22×C11 | C4×D3 | semidirect |
| 73. C3×C11 | C4×D4 | semidirect |
| 95. C22⋊C4 | D33 | semidirect |
| 99. C22×C3 | C4×D11 | semidirect |
| 109. C11 | #67⋊C4 | semidirect |
| 130. C22 | C4×D33 | semidirect |
| 137. C3 | (C22⋊D11)⋊C4 | 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 |
| C2×C4×D33 | 2 |
| C3×C11×C22⋊C4 | 2 |
| #10587203 | 2 |
| #10587201 | 2 |
| C4×Dic33 | 2 |
| (C22⋊D11)⋊C4 | 3 |
| #67⋊C4 | 11 |