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. C2×D220 | C2 | semidirect |
| 2. C2×C4×D5×C11 | C2 | semidirect |
| 3. C2×C5×Dic22 | C2 | semidirect |
| 4. C2×#89169 | C2 | semidirect |
| 5. C2×#89166 | C2 | semidirect |
| 6. #11724986 | C2 | direct (N × H) |
| 10. D220 | C22 | semidirect |
| 12. C4×D5×C11 | C22 | semidirect |
| 14. C5×Dic22 | C22 | semidirect |
| 15. #89169 | C22 | semidirect |
| 16. #89166 | C22 | semidirect |
| 31. C2×Dic22 | D5 | semidirect |
| 33. C2×C5×C11 | #41 | semidirect |
| 46. Dic22 | C2×D5 | semidirect |
| 52. C2×C4×D5 | D11 | semidirect |
| 53. C5×C11 | C2×#41 | semidirect |
| 71. C4×D5 | C2×D11 | semidirect |
| 74. C2×C11 | #713 | semidirect |
| 91. C11 | C2×#713 | semidirect |
| 92. C2×C5 | #4339 | semidirect |
| 106. C5 | C2×#4339 | semidirect |
| 117. C2 | #11724986 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D220 | 2 |
| C2×C4×D5×C11 | 2 |
| C2×C5×Dic22 | 2 |
| C2×#89169 | 2 |
| C2×#89166 | 2 |
| #11724986 | 2 |
| C2×#4339 | 5 |
| C2×#713 | 11 |