Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
136 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 47 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. #11725031 | C2 | semidirect |
| 2. C2×D220 | C2 | semidirect |
| 3. C5×C11×M16 | C2 | semidirect |
| 4. D440 | C2 | semidirect |
| 5. #11724924 | C2 | semidirect |
| 11. D220 | C22 | semidirect |
| 13. Dic110 | C22 | semidirect |
| 14. C5×C8×C11 | C22 | semidirect |
| 25. C11×M16 | D5 | semidirect |
| 41. C8×C11 | C2×D5 | semidirect |
| 44. C5×M16 | D11 | semidirect |
| 47. C5×C11 | AGL(1,ℤ/8) | semidirect |
| 63. C5×C8 | C2×D11 | semidirect |
| 80. M16 | D55 | semidirect |
| 81. C11 | #4054 | semidirect |
| 94. C8 | C2×D55 | semidirect |
| 95. C5 | #66961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11725031 | 2 |
| C2×D220 | 2 |
| C5×C11×M16 | 2 |
| D440 | 2 |
| #11724924 | 2 |
| #66961 | 5 |
| #4054 | 11 |