Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
136 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 57 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. #11724928 | C2 | semidirect |
| 4. #11724923 | C2 | semidirect |
| 5. C8×D55 | C2 | semidirect |
| 13. C5×C8×C11 | C22 | semidirect |
| 14. C11⋊#168 | C22 | semidirect |
| 25. C11×M16 | D5 | semidirect |
| 33. D55 | M16 | direct (N × H) |
| 41. C8×C11 | C2×D5 | semidirect |
| 44. C5×M16 | D11 | semidirect |
| 48. C5×C11 | C2×M16 | semidirect |
| 64. C5×C8 | C2×D11 | semidirect |
| 82. M16 | D55 | direct (N × H) |
| 84. C11 | D5×M16 | semidirect |
| 97. C8 | C2×D55 | semidirect |
| 98. C5 | M16×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D55 | 2 |
| C5×C11×M16 | 2 |
| #11724928 | 2 |
| #11724923 | 2 |
| C8×D55 | 2 |
| M16×D11 | 5 |
| D5×M16 | 11 |