Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
156 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 55 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. C22×C4×C5×C11 | C2 | semidirect |
| 3. C22⋊Dic55 | C2 | semidirect |
| 4. #11724932 | C2 | semidirect |
| 5. #11724930 | C2 | semidirect |
| 22. C22×C4×C11 | D5 | semidirect |
| 39. C22×C4×C5 | D11 | semidirect |
| 44. C5×C11 | #123 | semidirect |
| 74. C22×C4 | D55 | semidirect |
| 78. C11 | #4075 | semidirect |
| 90. C5 | #66982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×C11 | 2 |
| C2×C22⋊D55 | 2 |
| C22⋊Dic55 | 2 |
| #11724932 | 2 |
| #11724930 | 2 |
| #66982 | 5 |
| #4075 | 11 |