Finite Group DatabasebetaFinite Group DatabasebetaOrder 1056.
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 30. C3×Dic11 | Q8 | semidirect |
| 32. C11×Dic3 | Q8 | semidirect |
| 60. Dic11 | Dic6 | semidirect |
| 61. C3×C11 | C4⋊Q8 | semidirect |
| 89. Dic3 | Dic22 | semidirect |
| 90. C11 | #888 | semidirect |
| 111. C3 | #66941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic66 | 2 |
| C2×#63143 | 2 |
| C11×Dic3⋊C4 | 2 |
| C3×Dic11⋊C4 | 2 |
| Dic3⋊Dic11 | 2 |
| Dic11⋊Dic3 | 2 |
| Dic3×Dic11 | 2 |
| #66941 | 3 |
| #888 | 11 |