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. C11×Dic3⋊C4 | C2 | semidirect |
| 5. Dic11⋊Dic3 | C2 | semidirect |
| 28. C2×C3×D11 | Q8 | semidirect |
| 55. Dic3⋊C4 | D11 | semidirect |
| 59. C2×D11 | Dic6 | semidirect |
| 66. C3×C11 | C22⋊Q8 | semidirect |
| 98. C11 | #924 | semidirect |
| 122. C3 | #66949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D11 | 2 |
| C2×#63143 | 2 |
| #10587201 | 2 |
| C11×Dic3⋊C4 | 2 |
| Dic11⋊Dic3 | 2 |
| (C2×D11)⋊Dic3 | 2 |
| #66949 | 3 |
| #924 | 11 |