Finite Group DatabasebetaFinite Group DatabasebetaOrder 1056.
152 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 48 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. C2×C3×Dic22 | C2 | semidirect |
| 3. #10587203 | C2 | semidirect |
| 4. C11×(C2×D3)⋊C4 | C2 | semidirect |
| 5. #10587156 | C2 | semidirect |
| 6. (C2×D3)⋊Dic11 | C2 | semidirect |
| 7. Dic3×Dic11 | C2 | semidirect |
| 19. C2×Dic22 | D3 | semidirect |
| 57. (C2×D3)⋊C4 | D11 | semidirect |
| 71. C3×C11 | #124 | semidirect |
| 106. C11 | #947 | semidirect |
| 133. C3 | #66938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic22 | 2 |
| C2×#63142 | 2 |
| #10587203 | 2 |
| C11×(C2×D3)⋊C4 | 2 |
| #10587156 | 2 |
| (C2×D3)⋊Dic11 | 2 |
| Dic3×Dic11 | 2 |
| #66938 | 3 |
| #947 | 11 |