Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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. C11×#713 | C2 | semidirect |
| 2. D4×D5×C11 | C2 | semidirect |
| 3. C5×C11×SD16 | C2 | semidirect |
| 4. C11×#688 | C2 | semidirect |
| 5. C11×#686 | C2 | semidirect |
| 6. C11×D40 | C2 | semidirect |
| 7. C11×#676 | C2 | semidirect |
| 9. C5×Q8×C11 | C22 | semidirect |
| 14. C11×D20 | C22 | semidirect |
| 17. C5×C8×C11 | C22 | semidirect |
| 18. C11×#168 | C22 | semidirect |
| 31. C11×SD16 | D5 | semidirect |
| 35. #4060 | C11 | direct (N × H) |
| 42. Q8×C11 | C2×D5 | semidirect |
| 51. C8×C11 | C2×D5 | semidirect |
| 52. #713 | C2×C11 | semidirect |
| 53. D4×D5 | C2×C11 | semidirect |
| 54. C5×SD16 | C2×C11 | semidirect |
| 55. #688 | C2×C11 | semidirect |
| 56. #686 | C2×C11 | semidirect |
| 57. D40 | C2×C11 | semidirect |
| 58. #676 | C2×C11 | semidirect |
| 59. C5×C11 | AGL(1,ℤ/8) | semidirect |
| 69. C5×Q8 | C22×C11 | semidirect |
| 74. D20 | C22×C11 | semidirect |
| 77. C5×C8 | C22×C11 | semidirect |
| 78. #168 | C22×C11 | semidirect |
| 96. SD16 | D5×C11 | semidirect |
| 100. C11 | #4060 | direct (N × H) |
| 107. Q8 | C2×D5×C11 | semidirect |
| 116. C8 | C2×D5×C11 | semidirect |
| 117. C5 | C11×AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#713 | 2 |
| D4×D5×C11 | 2 |
| C5×C11×SD16 | 2 |
| C11×#688 | 2 |
| C11×#686 | 2 |
| C11×D40 | 2 |
| C11×#676 | 2 |
| C11×AGL(1,ℤ/8) | 5 |
| #4060 | 11 |