Finite Group DatabasebetaFinite Group DatabasebetaOrder 1056.
124 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 124 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. #10587281 | C2 | semidirect |
| 2. #10587230 | C2 | semidirect |
| 3. C11×#213 | C2 | semidirect |
| 4. C3×#4324 | C2 | semidirect |
| 5. #10587151 | C2 | semidirect |
| 6. #10587148 | C2 | semidirect |
| 7. D33⋊C8 | C2 | semidirect |
| 24. #4324 | D3 | semidirect |
| 54. #213 | D11 | semidirect |
| 64. C3×C11 | #135 | semidirect |
| 95. C11 | #916 | semidirect |
| 118. C3 | #66965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10587281 | 2 |
| #10587230 | 2 |
| C11×#213 | 2 |
| C3×#4324 | 2 |
| #10587151 | 2 |
| #10587148 | 2 |
| D33⋊C8 | 2 |
| #66965 | 3 |
| #916 | 11 |