Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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×D5×C11 | C2 | semidirect |
| 3. C5×C11×SD16 | C2 | semidirect |
| 4. C11×#688 | C2 | semidirect |
| 5. C11×#687 | C2 | semidirect |
| 6. C11×#677 | C2 | semidirect |
| 7. C8×D5×C11 | C2 | semidirect |
| 9. C5×Q8×C11 | C22 | semidirect |
| 16. C11×Dic10 | C22 | semidirect |
| 17. C5×C8×C11 | C22 | semidirect |
| 18. C11×#168 | C22 | semidirect |
| 33. C11×SD16 | D5 | direct (N × H) |
| 35. D5×SD16 | C11 | direct (N × H) |
| 39. D5×C11 | SD16 | direct (N × H) |
| 43. Q8×C11 | C2×D5 | semidirect |
| 50. C8×C11 | C2×D5 | semidirect |
| 51. Q8×D5 | C2×C11 | semidirect |
| 53. C5×SD16 | C2×C11 | semidirect |
| 54. #688 | C2×C11 | semidirect |
| 55. #687 | C2×C11 | semidirect |
| 56. #677 | C2×C11 | semidirect |
| 57. C8×D5 | C2×C11 | semidirect |
| 58. C5×C11 | C2×SD16 | semidirect |
| 68. C5×Q8 | C22×C11 | semidirect |
| 75. Dic10 | C22×C11 | semidirect |
| 76. C5×C8 | C22×C11 | semidirect |
| 77. #168 | C22×C11 | semidirect |
| 96. SD16 | D5×C11 | direct (N × H) |
| 98. C11 | D5×SD16 | direct (N × H) |
| 102. D5 | C11×SD16 | direct (N × H) |
| 106. Q8 | C2×D5×C11 | semidirect |
| 113. C8 | C2×D5×C11 | semidirect |
| 114. C5 | C2×C11×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D5×C11 | 2 |
| D4×D5×C11 | 2 |
| C5×C11×SD16 | 2 |
| C11×#688 | 2 |
| C11×#687 | 2 |
| C11×#677 | 2 |
| C8×D5×C11 | 2 |
| C2×C11×SD16 | 5 |
| D5×SD16 | 11 |