Finite Group DatabasebetaFinite Group DatabasebetaOrder 1056.
148 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 52 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. C2×#63143 | C2 | semidirect |
| 3. #10587201 | C2 | semidirect |
| 4. C3×Dic11⋊C4 | C2 | semidirect |
| 5. Dic3⋊Dic11 | C2 | semidirect |
| 24. Dic11⋊C4 | D3 | semidirect |
| 28. C2×D3×C11 | Q8 | semidirect |
| 66. C3×C11 | C22⋊Q8 | semidirect |
| 91. C2×D3 | Dic22 | semidirect |
| 98. C11 | #896 | semidirect |
| 122. C3 | #66977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D3×C11 | 2 |
| C2×#63143 | 2 |
| #10587201 | 2 |
| C3×Dic11⋊C4 | 2 |
| Dic3⋊Dic11 | 2 |
| (C2×D3)⋊Dic11 | 2 |
| #66977 | 3 |
| #896 | 11 |