Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
328 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 116 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×Dic55 | C2 | semidirect |
| 2. C2×C11×C22⋊D5 | C2 | semidirect |
| 3. C2×C5×C22⋊D11 | C2 | semidirect |
| 4. C2×#89170 | C2 | semidirect |
| 5. C2×#89167 | C2 | semidirect |
| 6. C2×D5×Dic11 | C2 | semidirect |
| 7. #11724997 | C2 | direct (N × H) |
| 8. C2×Dic5×D11 | C2 | semidirect |
| 14. C2×Dic55 | C22 | semidirect |
| 15. C11×C22⋊D5 | C22 | semidirect |
| 17. C5×C22⋊D11 | C22 | semidirect |
| 19. #89170 | C22 | semidirect |
| 20. #89167 | C22 | semidirect |
| 21. D5×Dic11 | C22 | semidirect |
| 22. Dic5×D11 | C22 | semidirect |
| 37. C2×C22⋊D11 | D5 | semidirect |
| 45. C2×C5×C11 | #41 | semidirect |
| 55. C22⋊D11 | C2×D5 | semidirect |
| 65. C2×C22⋊D5 | D11 | semidirect |
| 71. C5×C11 | C2×#41 | semidirect |
| 89. C22⋊D5 | C2×D11 | semidirect |
| 100. C2×C11 | #711 | semidirect |
| 122. C11 | C2×#711 | semidirect |
| 125. C2×C5 | #4341 | semidirect |
| 142. C5 | C2×#4341 | semidirect |
| 157. C2 | #11724997 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic55 | 2 |
| C2×C11×C22⋊D5 | 2 |
| C2×C5×C22⋊D11 | 2 |
| C2×#89170 | 2 |
| C2×#89167 | 2 |
| C2×D5×Dic11 | 2 |
| #11724997 | 2 |
| C2×Dic5×D11 | 2 |
| C2×#4341 | 5 |
| C2×#711 | 11 |