Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
136 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 41 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. #11725035 | C2 | semidirect |
| 2. D4×D55 | C2 | semidirect |
| 3. C5×C11×SD16 | C2 | semidirect |
| 4. #11724935 | C2 | semidirect |
| 5. #11724933 | C2 | semidirect |
| 6. D440 | C2 | semidirect |
| 7. #11724923 | C2 | semidirect |
| 9. C5×Q8×C11 | C22 | semidirect |
| 14. D220 | C22 | semidirect |
| 17. C5×C8×C11 | C22 | semidirect |
| 18. C11⋊#168 | C22 | semidirect |
| 30. C11×SD16 | D5 | semidirect |
| 42. Q8×C11 | C2×D5 | semidirect |
| 50. C8×C11 | C2×D5 | semidirect |
| 54. C5×SD16 | D11 | semidirect |
| 59. C5×C11 | AGL(1,ℤ/8) | semidirect |
| 69. C5×Q8 | C2×D11 | semidirect |
| 77. C5×C8 | C2×D11 | semidirect |
| 96. SD16 | D55 | semidirect |
| 100. C11 | #4060 | semidirect |
| 107. Q8 | C2×D55 | semidirect |
| 116. C8 | C2×D55 | semidirect |
| 117. C5 | #66967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11725035 | 2 |
| D4×D55 | 2 |
| C5×C11×SD16 | 2 |
| #11724935 | 2 |
| #11724933 | 2 |
| D440 | 2 |
| #11724923 | 2 |
| #66967 | 5 |
| #4060 | 11 |