Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
136 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 136 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 |
|---|---|---|
| 2. C11×#704 | C2 | semidirect |
| 3. C11×#700 | C2 | semidirect |
| 4. C11×D5⋊C8 | C2 | semidirect |
| 12. C11×#170 | C22 | semidirect |
| 26. D5⋊M16 | C11 | direct (N × H) |
| 30. D5×C11 | M16 | semidirect |
| 40. #704 | C2×C11 | semidirect |
| 41. #700 | C2×C11 | semidirect |
| 42. D5⋊C8 | C2×C11 | semidirect |
| 43. C5×C11 | C2×M16 | semidirect |
| 59. #170 | C22×C11 | semidirect |
| 77. C11 | D5⋊M16 | direct (N × H) |
| 81. D5 | C11×M16 | semidirect |
| 90. 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 |
| C11×#704 | 2 |
| C11×#700 | 2 |
| C11×D5⋊C8 | 2 |
| C2×C11×M16 | 5 |
| D5⋊M16 | 11 |