Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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. Q8×D55 | C2 | semidirect |
| 3. C5×C11×SD16 | C2 | semidirect |
| 4. #11724936 | C2 | semidirect |
| 5. #11724934 | C2 | semidirect |
| 6. Dic220 | C2 | semidirect |
| 7. #11724923 | C2 | semidirect |
| 29. C11×SD16 | D5 | semidirect |
| 51. C5×SD16 | D11 | semidirect |
| 56. C5×C11 | #137 | semidirect |
| 91. SD16 | D55 | semidirect |
| 93. C11 | #4061 | semidirect |
| 108. C5 | #66968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D55 | 2 |
| #11725033 | 2 |
| C5×C11×SD16 | 2 |
| #11724936 | 2 |
| #11724934 | 2 |
| Dic220 | 2 |
| #11724923 | 2 |
| #66968 | 5 |
| #4061 | 11 |