Finite Group DatabasebetaFinite Group DatabasebetaOrder 1056.
140 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 16. #63143 | C4 | direct (N × H) |
| 25. C3×C4×C11 | Q8 | semidirect |
| 54. C4×C11 | Dic6 | semidirect |
| 59. C3×C11 | C4×Q8 | semidirect |
| 82. C3×C4 | Dic22 | semidirect |
| 87. C11 | C4×Dic6 | semidirect |
| 106. C4 | #63143 | direct (N × H) |
| 107. C3 | C4×Dic22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63143 | 2 |
| C4×Dic33 | 2 |
| C4×C11×Dic3 | 2 |
| C3×C4×Dic11 | 2 |
| Dic3⋊Dic11 | 2 |
| #10587158 | 2 |
| Dic11⋊Dic3 | 2 |
| C4×Dic22 | 3 |
| C4×Dic6 | 11 |