Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
136 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 43 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×D55 | C2 | semidirect |
| 3. C5×C11×SD16 | C2 | semidirect |
| 4. #11724935 | C2 | semidirect |
| 5. #11724934 | C2 | semidirect |
| 6. #11724924 | C2 | semidirect |
| 7. C8×D55 | C2 | semidirect |
| 9. C5×Q8×C11 | C22 | semidirect |
| 16. Dic110 | C22 | semidirect |
| 17. C5×C8×C11 | C22 | semidirect |
| 18. C11⋊#168 | C22 | semidirect |
| 30. C11×SD16 | D5 | semidirect |
| 39. D55 | SD16 | direct (N × H) |
| 41. Q8×C11 | C2×D5 | semidirect |
| 49. C8×C11 | C2×D5 | semidirect |
| 53. C5×SD16 | D11 | semidirect |
| 58. C5×C11 | C2×SD16 | semidirect |
| 68. C5×Q8 | C2×D11 | semidirect |
| 76. C5×C8 | C2×D11 | semidirect |
| 96. SD16 | D55 | direct (N × H) |
| 98. C11 | D5×SD16 | semidirect |
| 106. Q8 | C2×D55 | semidirect |
| 113. C8 | C2×D55 | semidirect |
| 114. C5 | SD16×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D55 | 2 |
| D4×D55 | 2 |
| C5×C11×SD16 | 2 |
| #11724935 | 2 |
| #11724934 | 2 |
| #11724924 | 2 |
| C8×D55 | 2 |
| SD16×D11 | 5 |
| D5×SD16 | 11 |