Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
148 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 1. C2×#89170 | C2 | semidirect |
| 4. C11×C4⋊Dic5 | C2 | semidirect |
| 5. C5×Dic11⋊C4 | C2 | semidirect |
| 6. Dic11⋊Dic5 | C2 | semidirect |
| 21. C2×D55 | Q8 | semidirect |
| 34. Dic11⋊C4 | D5 | semidirect |
| 55. C4⋊Dic5 | D11 | semidirect |
| 56. C5×C11 | C22⋊Q8 | semidirect |
| 98. C11 | #4043 | semidirect |
| 112. C5 | #66949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89170 | 2 |
| C2×#89166 | 2 |
| #11724932 | 2 |
| C11×C4⋊Dic5 | 2 |
| C5×Dic11⋊C4 | 2 |
| Dic11⋊Dic5 | 2 |
| #11724886 | 2 |
| #66949 | 5 |
| #4043 | 11 |