Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
328 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 178 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×C4×C5×C11 | C2 | semidirect |
| 2. C2×C5×C22⋊D11 | C2 | semidirect |
| 3. C5×#4339 | C2 | direct (N × H) |
| 4. C2×C5×D44 | C2 | semidirect |
| 5. C2×C4×C5×D11 | C2 | semidirect |
| 6. C2×C5×Dic22 | C2 | semidirect |
| 11. C2×C4×C5×C11 | C22 | semidirect |
| 12. C5×C22⋊D11 | C22 | semidirect |
| 14. C5×D44 | C22 | semidirect |
| 15. C4×C5×D11 | C22 | semidirect |
| 16. C5×Dic22 | C22 | semidirect |
| 17. C2×#4339 | C5 | direct (N × H) |
| 26. C22×C4×C11 | C2×C5 | semidirect |
| 27. C2×C22⋊D11 | C2×C5 | semidirect |
| 28. #4339 | C2×C5 | direct (N × H) |
| 29. C2×D44 | C2×C5 | semidirect |
| 30. C2×C4×D11 | C2×C5 | semidirect |
| 31. C2×Dic22 | C2×C5 | semidirect |
| 34. C2×C5×C11 | #41 | semidirect |
| 41. C2×C4×C11 | C22×C5 | semidirect |
| 42. C22⋊D11 | C22×C5 | semidirect |
| 44. D44 | C22×C5 | semidirect |
| 45. C4×D11 | C22×C5 | semidirect |
| 46. Dic22 | C22×C5 | semidirect |
| 52. C22×C4×C5 | D11 | semidirect |
| 53. C5×C11 | C2×#41 | semidirect |
| 71. C2×C4×C5 | C2×D11 | semidirect |
| 74. C2×C11 | C5×#41 | semidirect |
| 90. C22×C4 | C5×D11 | semidirect |
| 91. C11 | C2×C5×#41 | semidirect |
| 94. C2×C5 | #4339 | direct (N × H) |
| 105. C2×C4 | C2×C5×D11 | semidirect |
| 106. C5 | C2×#4339 | direct (N × H) |
| 117. C2 | C5×#4339 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×C11 | 2 |
| C2×C5×C22⋊D11 | 2 |
| C5×#4339 | 2 |
| C2×C5×D44 | 2 |
| C2×C4×C5×D11 | 2 |
| C2×C5×Dic22 | 2 |
| C2×#4339 | 5 |
| C2×C5×#41 | 11 |