Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
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 |
|---|---|---|
| 15. #89170 | C4 | direct (N × H) |
| 18. C4×C5×C11 | Q8 | semidirect |
| 51. C5×C11 | C4×Q8 | semidirect |
| 55. C4×C11 | Dic10 | semidirect |
| 75. C4×C5 | Dic22 | semidirect |
| 87. C11 | C4×Dic10 | semidirect |
| 99. C5 | C4×Dic22 | semidirect |
| 107. C4 | #89170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89170 | 2 |
| C4×Dic55 | 2 |
| C4×C11×Dic5 | 2 |
| C4×C5×Dic11 | 2 |
| #11724889 | 2 |
| #11724888 | 2 |
| Dic11⋊Dic5 | 2 |
| C4×Dic22 | 5 |
| C4×Dic10 | 11 |