Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
188 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 2. C2×#89166 | C2 | semidirect |
| 3. C4×C11×Dic5 | C2 | semidirect |
| 4. C5×C4⋊Dic11 | C2 | semidirect |
| 5. #11724886 | C2 | semidirect |
| 8. D220 | C4 | semidirect |
| 17. C2×D55 | C2×C4 | semidirect |
| 18. C4×C5×C11 | C2×C4 | semidirect |
| 21. C11×Dic5 | D4 | semidirect |
| 26. C4⋊Dic11 | D5 | semidirect |
| 43. C4×Dic5 | D11 | semidirect |
| 44. C5×C11 | C4×D4 | semidirect |
| 51. C4×C11 | C4×D5 | semidirect |
| 70. C4×C5 | C4×D11 | semidirect |
| 72. Dic5 | D44 | semidirect |
| 78. C11 | #4039 | semidirect |
| 90. C5 | C4×D44 | semidirect |
| 98. C4 | #89166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D220 | 2 |
| C2×#89166 | 2 |
| C4×C11×Dic5 | 2 |
| C5×C4⋊Dic11 | 2 |
| #11724886 | 2 |
| C4×D44 | 5 |
| #4039 | 11 |