Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
328 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 178 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. C22×C4×C5×C11 | C2 | semidirect |
| 2. C2×C11×C22⋊D5 | C2 | semidirect |
| 3. C11×#709 | C2 | direct (N × H) |
| 4. C2×C11×D20 | C2 | semidirect |
| 5. C2×C4×D5×C11 | C2 | semidirect |
| 6. C2×C11×Dic10 | C2 | semidirect |
| 11. C2×C4×C5×C11 | C22 | semidirect |
| 12. C11×C22⋊D5 | C22 | semidirect |
| 14. C11×D20 | C22 | semidirect |
| 15. C4×D5×C11 | C22 | semidirect |
| 16. C11×Dic10 | C22 | semidirect |
| 31. C22×C4×C11 | D5 | semidirect |
| 32. C2×#709 | C11 | direct (N × H) |
| 34. C2×C5×C11 | #41 | semidirect |
| 46. C2×C4×C11 | C2×D5 | semidirect |
| 47. C22×C4×C5 | C2×C11 | semidirect |
| 48. C2×C22⋊D5 | C2×C11 | semidirect |
| 49. #709 | C2×C11 | direct (N × H) |
| 50. C2×D20 | C2×C11 | semidirect |
| 51. C2×C4×D5 | C2×C11 | semidirect |
| 52. C2×Dic10 | C2×C11 | semidirect |
| 53. C5×C11 | C2×#41 | semidirect |
| 66. C2×C4×C5 | C22×C11 | semidirect |
| 67. C22⋊D5 | C22×C11 | semidirect |
| 69. D20 | C22×C11 | semidirect |
| 70. C4×D5 | C22×C11 | semidirect |
| 71. Dic10 | C22×C11 | semidirect |
| 75. C2×C11 | #709 | direct (N × H) |
| 90. C22×C4 | D5×C11 | semidirect |
| 91. C11 | C2×#709 | direct (N × H) |
| 93. C2×C5 | C11×#41 | semidirect |
| 105. C2×C4 | C2×D5×C11 | semidirect |
| 106. C5 | C2×C11×#41 | semidirect |
| 117. C2 | C11×#709 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×C11 | 2 |
| C2×C11×C22⋊D5 | 2 |
| C11×#709 | 2 |
| C2×C11×D20 | 2 |
| C2×C4×D5×C11 | 2 |
| C2×C11×Dic10 | 2 |
| C2×C11×#41 | 5 |
| C2×#709 | 11 |