Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
124 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 46 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. #11724979 | C2 | semidirect |
| 3. C2×C11×#170 | C2 | semidirect |
| 4. #11724962 | C2 | semidirect |
| 5. #11724961 | C2 | semidirect |
| 6. #11724960 | C2 | semidirect |
| 7. D11×#170 | C2 | semidirect |
| 54. C2×#170 | D11 | semidirect |
| 57. C5×C11 | #131 | semidirect |
| 95. C11 | #4131 | semidirect |
| 111. C5 | #66954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724996 | 2 |
| #11724979 | 2 |
| C2×C11×#170 | 2 |
| #11724962 | 2 |
| #11724961 | 2 |
| #11724960 | 2 |
| D11×#170 | 2 |
| #66954 | 5 |
| #4131 | 11 |