Finite Group DatabasebetaFinite Group DatabasebetaOrder 1056.
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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. D3×Dic22 | C2 | semidirect |
| 3. #10587195 | C2 | semidirect |
| 4. C11×ΓL(1,𝔽25) | C2 | semidirect |
| 5. C3×Dic44 | C2 | semidirect |
| 6. #10587151 | C2 | semidirect |
| 7. #10587147 | C2 | semidirect |
| 24. Dic44 | D3 | semidirect |
| 55. ΓL(1,𝔽25) | D11 | semidirect |
| 63. C3×C11 | #137 | semidirect |
| 93. C11 | #918 | semidirect |
| 115. C3 | #66962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10587231 | 2 |
| D3×Dic22 | 2 |
| #10587195 | 2 |
| C11×ΓL(1,𝔽25) | 2 |
| C3×Dic44 | 2 |
| #10587151 | 2 |
| #10587147 | 2 |
| #66962 | 3 |
| #918 | 11 |