Finite Group DatabasebetaFinite Group DatabasebetaOrder 1056.
136 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 38 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. D4×D33 | C2 | semidirect |
| 2. #10587230 | C2 | semidirect |
| 3. C11×#213 | C2 | semidirect |
| 4. C3×#4324 | C2 | semidirect |
| 5. #10587147 | C2 | semidirect |
| 6. #10587143 | C2 | semidirect |
| 7. #10587140 | C2 | semidirect |
| 14. C11×D12 | C22 | semidirect |
| 15. C3×Dic22 | C22 | semidirect |
| 18. C3×C11⋊C8 | C22 | semidirect |
| 19. C11×C3⋊C8 | C22 | semidirect |
| 23. #4324 | D3 | semidirect |
| 44. Dic22 | C2×D3 | semidirect |
| 46. C11⋊C8 | C2×D3 | semidirect |
| 56. #213 | D11 | semidirect |
| 67. C3×C11 | AGL(1,ℤ/8) | semidirect |
| 75. D12 | C2×D11 | semidirect |
| 79. C3⋊C8 | C2×D11 | semidirect |
| 100. C11 | #914 | semidirect |
| 125. C3 | #66964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D33 | 2 |
| #10587230 | 2 |
| C11×#213 | 2 |
| C3×#4324 | 2 |
| #10587147 | 2 |
| #10587143 | 2 |
| #10587140 | 2 |
| #66964 | 3 |
| #914 | 11 |