Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
312 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 122 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. Q8×D55 | C2 | semidirect |
| 2. Q8×D5×C11 | C2 | semidirect |
| 3. C5×Q8×D11 | C2 | semidirect |
| 5. D55⋊Q8 | C2 | semidirect |
| 6. D5×Dic22 | C2 | semidirect |
| 7. D11×Dic10 | C2 | semidirect |
| 9. C5×Q8×C11 | C22 | semidirect |
| 11. Dic110 | C22 | semidirect |
| 13. C11×Dic10 | C22 | semidirect |
| 15. C5×Dic22 | C22 | semidirect |
| 16. #89170 | C22 | semidirect |
| 24. D5×D11 | Q8 | direct (N × H) |
| 33. Q8×D11 | D5 | direct (N × H) |
| 38. D55 | C2×Q8 | semidirect |
| 39. C5×D11 | C2×Q8 | semidirect |
| 40. D5×C11 | C2×Q8 | semidirect |
| 43. Q8×C11 | C2×D5 | semidirect |
| 52. Dic22 | C2×D5 | semidirect |
| 57. Q8×D5 | D11 | direct (N × H) |
| 60. C5×C11 | C22×Q8 | semidirect |
| 71. C5×Q8 | C2×D11 | semidirect |
| 80. Dic10 | C2×D11 | semidirect |
| 85. D11 | Q8×D5 | direct (N × H) |
| 101. C11 | C2×Q8×D5 | semidirect |
| 105. D5 | Q8×D11 | direct (N × H) |
| 111. Q8 | D5×D11 | direct (N × H) |
| 118. C5 | C2×Q8×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D55 | 2 |
| Q8×D5×C11 | 2 |
| C5×Q8×D11 | 2 |
| C4×D5×D11 | 2 |
| D55⋊Q8 | 2 |
| D5×Dic22 | 2 |
| D11×Dic10 | 2 |
| C2×Q8×D11 | 5 |
| C2×Q8×D5 | 11 |