Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×D8×D29 | C2 | semidirect |
| 2. C2×#11745263 | C2 | semidirect |
| 3. #14271729 | C2 | semidirect |
| 4. #14271415 | C2 | semidirect |
| 5. #14271414 | C2 | semidirect |
| 6. #14271400 | C2 | semidirect |
| 7. #14271399 | C2 | semidirect |
| 8. #14271396 | C2 | semidirect |
| 9. #14271200 | C2 | semidirect |
| 10. #14271166 | C2 | semidirect |
| 11. C29×#466 | C2 | semidirect |
| 15. C22×C8×C29 | C22 | semidirect |
| 16. C29×#121 | C22 | semidirect |
| 18. #11745300 | C22 | semidirect |
| 21. #11745292 | C22 | semidirect |
| 22. C2×#90777 | C22 | semidirect |
| 27. C2×#90772 | C22 | semidirect |
| 29. C2×C8×D29 | C22 | semidirect |
| 30. #11745257 | C22 | semidirect |
| 34. C29×#107 | C22 | semidirect |
| 35. C29×#102 | C22 | semidirect |
| 36. #11745180 | C22 | semidirect |
| 37. #11745169 | C22 | semidirect |
| 38. #11745166 | C22 | semidirect |
| 39. #11745157 | C22 | semidirect |
| 40. #11745156 | C22 | semidirect |
| 80. C8×D29 | D4 | semidirect |
| 151. #466 | D29 | semidirect |
| 174. C22×C8 | C2×D29 | semidirect |
| 180. #121 | C2×D29 | semidirect |
| 185. #107 | C2×D29 | semidirect |
| 190. #102 | C2×D29 | semidirect |
| 191. C29 | #3058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D29 | 2 |
| C2×#11745263 | 2 |
| #14271729 | 2 |
| #14271415 | 2 |
| #14271414 | 2 |
| #14271400 | 2 |
| #14271399 | 2 |
| #14271396 | 2 |
| #14271200 | 2 |
| #14271166 | 2 |
| C29×#466 | 2 |
| #3058 | 29 |