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. C22×C11×Dic5 | C2 | semidirect |
| 3. C2×#89166 | C2 | semidirect |
| 4. C5×C22⋊Dic11 | C2 | semidirect |
| 5. #11724888 | C2 | semidirect |
| 6. #11724886 | C2 | semidirect |
| 7. Dic5×Dic11 | C2 | semidirect |
| 10. C22⋊D55 | C4 | semidirect |
| 21. C22×C5×C11 | C2×C4 | semidirect |
| 25. C2×D55 | C2×C4 | semidirect |
| 26. Dic55 | C2×C4 | semidirect |
| 30. C11×Dic5 | D4 | semidirect |
| 34. C22⋊Dic11 | D5 | semidirect |
| 55. C22×Dic5 | D11 | semidirect |
| 61. C5×C11 | C4×D4 | semidirect |
| 64. C22×C11 | C4×D5 | semidirect |
| 92. C22×C5 | C4×D11 | semidirect |
| 101. Dic5 | C22⋊D11 | semidirect |
| 109. C11 | #4027 | semidirect |
| 125. C5 | C4×C22⋊D11 | semidirect |
| 131. C22 | #89166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊D55 | 2 |
| C22×C11×Dic5 | 2 |
| C2×#89166 | 2 |
| C5×C22⋊Dic11 | 2 |
| #11724888 | 2 |
| #11724886 | 2 |
| Dic5×Dic11 | 2 |
| C4×C22⋊D11 | 5 |
| #4027 | 11 |