Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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×C5×D4×C11 | C2 | semidirect |
| 2. C11×#709 | C2 | semidirect |
| 3. C11×#687 | C2 | semidirect |
| 4. C11×#686 | C2 | semidirect |
| 5. C11×#681 | C2 | semidirect |
| 11. C11×D20 | C22 | semidirect |
| 13. C11×Dic10 | C22 | semidirect |
| 14. C11×#168 | C22 | semidirect |
| 24. C2×D4×C11 | D5 | semidirect |
| 28. #4078 | C11 | direct (N × H) |
| 42. C2×C5×D4 | C2×C11 | semidirect |
| 43. #709 | C2×C11 | semidirect |
| 44. #687 | C2×C11 | semidirect |
| 45. #686 | C2×C11 | semidirect |
| 46. #681 | C2×C11 | semidirect |
| 47. C5×C11 | AGL(1,ℤ/8) | semidirect |
| 60. D20 | C22×C11 | semidirect |
| 62. Dic10 | C22×C11 | semidirect |
| 63. #168 | C22×C11 | semidirect |
| 77. C2×D4 | D5×C11 | semidirect |
| 81. C11 | #4078 | direct (N × H) |
| 95. C5 | C11×AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×C11 | 2 |
| C11×#709 | 2 |
| C11×#687 | 2 |
| C11×#686 | 2 |
| C11×#681 | 2 |
| C11×AGL(1,ℤ/8) | 5 |
| #4078 | 11 |