Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
136 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 136 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. #11725033 | C2 | semidirect |
| 2. D4×D55 | C2 | semidirect |
| 3. C5×C11×D8 | C2 | semidirect |
| 4. #11724934 | C2 | semidirect |
| 5. #11724933 | C2 | semidirect |
| 6. #11724924 | C2 | semidirect |
| 7. #11724923 | C2 | semidirect |
| 10. C5×D4×C11 | C22 | semidirect |
| 16. Dic110 | C22 | semidirect |
| 17. C5×C8×C11 | C22 | semidirect |
| 18. C11⋊#168 | C22 | semidirect |
| 30. C11×D8 | D5 | semidirect |
| 43. D4×C11 | C2×D5 | semidirect |
| 50. C8×C11 | C2×D5 | semidirect |
| 54. C5×D8 | D11 | semidirect |
| 59. C5×C11 | AGL(1,ℤ/8) | semidirect |
| 70. C5×D4 | C2×D11 | semidirect |
| 77. C5×C8 | C2×D11 | semidirect |
| 98. D8 | D55 | semidirect |
| 100. C11 | #4057 | semidirect |
| 112. D4 | C2×D55 | semidirect |
| 116. C8 | C2×D55 | semidirect |
| 117. C5 | #66964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11725033 | 2 |
| D4×D55 | 2 |
| C5×C11×D8 | 2 |
| #11724934 | 2 |
| #11724933 | 2 |
| #11724924 | 2 |
| #11724923 | 2 |
| #66964 | 5 |
| #4057 | 11 |