Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
136 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 2. #11724975 | C2 | semidirect |
| 3. C11×#700 | C2 | semidirect |
| 4. #11724961 | C2 | semidirect |
| 5. #11724960 | C2 | semidirect |
| 13. C11⋊#170 | C22 | semidirect |
| 14. C11×#170 | C22 | semidirect |
| 31. D55 | M16 | semidirect |
| 46. #700 | D11 | semidirect |
| 48. C5×C11 | C2×M16 | semidirect |
| 65. #170 | C2×D11 | semidirect |
| 84. C11 | D5⋊M16 | semidirect |
| 98. C5 | M16×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D5×D11 | 2 |
| #11724975 | 2 |
| C11×#700 | 2 |
| #11724961 | 2 |
| #11724960 | 2 |
| M16×D11 | 5 |
| D5⋊M16 | 11 |