Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
136 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 136 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. D4×D55 | C2 | semidirect |
| 2. #11724985 | C2 | semidirect |
| 3. C11×#686 | C2 | semidirect |
| 4. C5×#4324 | C2 | semidirect |
| 5. #11724877 | C2 | semidirect |
| 6. #11724873 | C2 | semidirect |
| 7. #11724870 | C2 | semidirect |
| 13. C11×D20 | C22 | semidirect |
| 14. C5×Dic22 | C22 | semidirect |
| 17. C5×C11⋊C8 | C22 | semidirect |
| 18. C11×#168 | C22 | semidirect |
| 31. #4324 | D5 | semidirect |
| 49. Dic22 | C2×D5 | semidirect |
| 51. C11⋊C8 | C2×D5 | semidirect |
| 56. #686 | D11 | semidirect |
| 59. C5×C11 | AGL(1,ℤ/8) | semidirect |
| 74. D20 | C2×D11 | semidirect |
| 78. #168 | C2×D11 | semidirect |
| 100. C11 | #4060 | semidirect |
| 117. C5 | #66964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D55 | 2 |
| #11724985 | 2 |
| C11×#686 | 2 |
| C5×#4324 | 2 |
| #11724877 | 2 |
| #11724873 | 2 |
| #11724870 | 2 |
| #66964 | 5 |
| #4060 | 11 |