Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×C11×D20 | C2 | semidirect |
| 3. C11×#686 | C2 | direct (N × H) |
| 4. C2×C11×#168 | C2 | semidirect |
| 8. C5×D4×C11 | C22 | semidirect |
| 11. C11×D20 | C22 | semidirect |
| 12. C11×#168 | C22 | semidirect |
| 22. C2×D4×C11 | D5 | semidirect |
| 25. C2×#686 | C11 | direct (N × H) |
| 27. C2×C5×C11 | D8 | semidirect |
| 35. D4×C11 | C2×D5 | semidirect |
| 38. C2×C5×D4 | C2×C11 | semidirect |
| 39. C2×D20 | C2×C11 | semidirect |
| 40. #686 | C2×C11 | direct (N × H) |
| 41. C2×#168 | C2×C11 | semidirect |
| 42. C5×C11 | C2×D8 | semidirect |
| 53. C5×D4 | C22×C11 | semidirect |
| 56. D20 | C22×C11 | semidirect |
| 57. #168 | C22×C11 | semidirect |
| 61. C2×C11 | #686 | direct (N × H) |
| 71. C2×D4 | D5×C11 | semidirect |
| 74. C11 | C2×#686 | direct (N × H) |
| 76. C2×C5 | C11×D8 | semidirect |
| 84. D4 | C2×D5×C11 | semidirect |
| 87. C5 | C2×C11×D8 | semidirect |
| 97. C2 | C11×#686 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×C11 | 2 |
| C2×C11×D20 | 2 |
| C11×#686 | 2 |
| C2×C11×#168 | 2 |
| C2×C11×D8 | 5 |
| C2×#686 | 11 |