Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
136 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 78 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. C5×C11×M16 | C2 | semidirect |
| 3. C11×#681 | C2 | semidirect |
| 4. C11×#676 | C2 | semidirect |
| 5. C8×D5×C11 | C2 | semidirect |
| 13. C5×C8×C11 | C22 | semidirect |
| 14. C11×#168 | C22 | semidirect |
| 27. C11×M16 | D5 | direct (N × H) |
| 29. D5×M16 | C11 | direct (N × H) |
| 33. D5×C11 | M16 | direct (N × H) |
| 42. C8×C11 | C2×D5 | semidirect |
| 44. C5×M16 | C2×C11 | semidirect |
| 45. #681 | C2×C11 | semidirect |
| 46. #676 | C2×C11 | semidirect |
| 47. C8×D5 | C2×C11 | semidirect |
| 48. C5×C11 | C2×M16 | semidirect |
| 64. C5×C8 | C22×C11 | semidirect |
| 65. #168 | C22×C11 | semidirect |
| 82. M16 | D5×C11 | direct (N × H) |
| 84. C11 | D5×M16 | direct (N × H) |
| 88. D5 | C11×M16 | direct (N × H) |
| 97. C8 | C2×D5×C11 | semidirect |
| 98. C5 | C2×C11×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D5×C11 | 2 |
| C5×C11×M16 | 2 |
| C11×#681 | 2 |
| C11×#676 | 2 |
| C8×D5×C11 | 2 |
| C2×C11×M16 | 5 |
| D5×M16 | 11 |