Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
124 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 47 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×C11×#41 | C2 | semidirect |
| 2. #11725031 | C2 | semidirect |
| 3. #11724936 | C2 | semidirect |
| 4. #11724935 | C2 | semidirect |
| 5. #11724934 | C2 | semidirect |
| 6. #11724933 | C2 | semidirect |
| 7. C2×C11⋊#168 | C2 | semidirect |
| 27. C11×#41 | D5 | semidirect |
| 50. C5×#41 | D11 | semidirect |
| 57. C5×C11 | #135 | semidirect |
| 89. #41 | D55 | semidirect |
| 95. C11 | #4096 | semidirect |
| 111. C5 | #67003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C11×#41 | 2 |
| #11725031 | 2 |
| #11724936 | 2 |
| #11724935 | 2 |
| #11724934 | 2 |
| #11724933 | 2 |
| C2×C11⋊#168 | 2 |
| #67003 | 5 |
| #4096 | 11 |