Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
136 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 40 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. C5×D4×D11 | C2 | semidirect |
| 2. #11724990 | C2 | semidirect |
| 3. #11724933 | C2 | semidirect |
| 4. C11×#687 | C2 | semidirect |
| 5. #11724874 | C2 | semidirect |
| 6. #11724872 | C2 | semidirect |
| 7. #11724868 | C2 | semidirect |
| 10. D220 | C22 | semidirect |
| 11. C11×Dic10 | C22 | semidirect |
| 17. C11⋊#168 | C22 | semidirect |
| 18. C11×#168 | C22 | semidirect |
| 29. D4×D11 | D5 | semidirect |
| 55. #687 | D11 | semidirect |
| 59. C5×C11 | AGL(1,ℤ/8) | semidirect |
| 76. Dic10 | C2×D11 | semidirect |
| 78. #168 | C2×D11 | semidirect |
| 100. C11 | #4078 | semidirect |
| 117. C5 | #66967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×D11 | 2 |
| #11724990 | 2 |
| #11724933 | 2 |
| C11×#687 | 2 |
| #11724874 | 2 |
| #11724872 | 2 |
| #11724868 | 2 |
| #66967 | 5 |
| #4078 | 11 |