Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
188 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 72 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×C11×Dic5 | C2 | semidirect |
| 3. C2×Dic5×D11 | C2 | semidirect |
| 4. C22⋊Dic55 | C2 | semidirect |
| 5. Dic11⋊Dic5 | C2 | semidirect |
| 6. (C2×D11)⋊Dic5 | C2 | semidirect |
| 7. Dic5×Dic11 | C2 | semidirect |
| 15. C5×C22⋊D11 | C4 | semidirect |
| 21. C22×C5×C11 | C2×C4 | semidirect |
| 25. C2×C5×D11 | C2×C4 | semidirect |
| 28. C5×Dic11 | C2×C4 | semidirect |
| 30. C11×Dic5 | D4 | semidirect |
| 49. C22⋊D11 | Dic5 | direct (N × H) |
| 56. C22×Dic5 | D11 | semidirect |
| 61. C5×C11 | C4×D4 | semidirect |
| 64. C22×C11 | C2×Dic5 | semidirect |
| 68. C2×D11 | C2×Dic5 | semidirect |
| 73. Dic11 | C2×Dic5 | semidirect |
| 95. C22×C5 | C4×D11 | semidirect |
| 101. Dic5 | C22⋊D11 | direct (N × H) |
| 109. C11 | D4×Dic5 | semidirect |
| 125. C5 | C4×C22⋊D11 | semidirect |
| 131. C22 | Dic5×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×Dic5 | 2 |
| C2×C5×C22⋊D11 | 2 |
| C2×Dic5×D11 | 2 |
| C22⋊Dic55 | 2 |
| Dic11⋊Dic5 | 2 |
| (C2×D11)⋊Dic5 | 2 |
| Dic5×Dic11 | 2 |
| C4×C22⋊D11 | 5 |
| D4×Dic5 | 11 |