Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
312 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 132 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. C2×Dic110 | C2 | semidirect |
| 2. C2×C11×Dic10 | C2 | semidirect |
| 4. C2×#89170 | C2 | semidirect |
| 6. D11×Dic10 | C2 | direct (N × H) |
| 10. Dic110 | C22 | semidirect |
| 12. C11×Dic10 | C22 | semidirect |
| 15. #89170 | C22 | semidirect |
| 19. C2×C5×D11 | Q8 | semidirect |
| 32. C2×C5×C11 | C2×Q8 | semidirect |
| 34. C5×D11 | C2×Q8 | semidirect |
| 50. C2×Dic10 | D11 | direct (N × H) |
| 51. C5×C11 | C22×Q8 | semidirect |
| 53. C2×D11 | Dic10 | direct (N × H) |
| 68. Dic10 | C2×D11 | direct (N × H) |
| 70. C2×C11 | C2×Dic10 | semidirect |
| 72. D11 | C2×Dic10 | direct (N × H) |
| 86. C11 | C22×Dic10 | semidirect |
| 88. C2×C5 | Q8×D11 | semidirect |
| 100. C5 | C2×Q8×D11 | semidirect |
| 109. C2 | D11×Dic10 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic110 | 2 |
| C2×C11×Dic10 | 2 |
| C2×C4×C5×D11 | 2 |
| C2×#89170 | 2 |
| C2×Dic5×D11 | 2 |
| D11×Dic10 | 2 |
| C2×Q8×D11 | 5 |
| C22×Dic10 | 11 |