Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
188 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 102 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. C22×C11×Dic5 | C2 | semidirect |
| 3. C11×C22⋊Dic5 | C2 | semidirect |
| 4. C11×C4⋊Dic5 | C2 | semidirect |
| 5. C4×C11×Dic5 | C2 | semidirect |
| 7. C5×D4×C11 | C4 | semidirect |
| 16. C22×C5×C11 | C2×C4 | semidirect |
| 18. C4×C5×C11 | C2×C4 | semidirect |
| 21. C11×Dic5 | D4 | direct (N × H) |
| 27. D4×Dic5 | C11 | direct (N × H) |
| 33. D4×C11 | Dic5 | direct (N × H) |
| 40. C22×Dic5 | C2×C11 | semidirect |
| 41. C22⋊Dic5 | C2×C11 | semidirect |
| 42. C4⋊Dic5 | C2×C11 | semidirect |
| 43. C4×Dic5 | C2×C11 | semidirect |
| 44. C5×C11 | C4×D4 | semidirect |
| 47. C22×C11 | C2×Dic5 | semidirect |
| 52. C4×C11 | C2×Dic5 | semidirect |
| 54. C5×D4 | C4×C11 | semidirect |
| 67. C22×C5 | C2×C4×C11 | semidirect |
| 69. C4×C5 | C2×C4×C11 | semidirect |
| 72. Dic5 | D4×C11 | direct (N × H) |
| 78. C11 | D4×Dic5 | direct (N × H) |
| 84. D4 | C11×Dic5 | direct (N × H) |
| 90. C5 | C4×D4×C11 | semidirect |
| 93. C22 | C2×C11×Dic5 | semidirect |
| 98. C4 | C2×C11×Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×C11 | 2 |
| C22×C11×Dic5 | 2 |
| C11×C22⋊Dic5 | 2 |
| C11×C4⋊Dic5 | 2 |
| C4×C11×Dic5 | 2 |
| C4×D4×C11 | 5 |
| D4×Dic5 | 11 |