Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
120 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 38 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. C11×#688 | C2 | semidirect |
| 4. C5×#4326 | C2 | semidirect |
| 5. #11724881 | C2 | semidirect |
| 6. #11724878 | C2 | semidirect |
| 7. #11724870 | C2 | semidirect |
| 30. #4326 | D5 | semidirect |
| 53. #688 | D11 | semidirect |
| 56. C5×C11 | #137 | semidirect |
| 93. C11 | #4064 | 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 |
| #11724985 | 2 |
| C11×#688 | 2 |
| C5×#4326 | 2 |
| #11724881 | 2 |
| #11724878 | 2 |
| #11724870 | 2 |
| #66968 | 5 |
| #4064 | 11 |