Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271873 | C2 | semidirect |
| 3. #14271510 | C2 | semidirect |
| 4. #14271483 | C2 | semidirect |
| 5. #14271453 | C2 | semidirect |
| 6. #14271395 | C2 | semidirect |
| 7. #14271363 | C2 | semidirect |
| 8. #14271312 | C2 | semidirect |
| 9. C8×D116 | C2 | semidirect |
| 10. #102×D29 | C2 | semidirect |
| 11. C4×SD16×C29 | C2 | semidirect |
| 15. C4×Q8×C29 | C22 | semidirect |
| 17. #11745308 | C22 | semidirect |
| 18. C2×#90784 | C22 | semidirect |
| 20. C2×C8×D29 | C22 | semidirect |
| 23. C4⋊C4×D29 | C22 | semidirect |
| 29. #11745231 | C22 | semidirect |
| 30. C29×#106 | C22 | semidirect |
| 31. C29×#103 | C22 | semidirect |
| 33. C4×C8×C29 | C22 | semidirect |
| 35. #11745169 | C22 | semidirect |
| 36. #11745169 | C22 | semidirect |
| 37. #11745168 | C22 | semidirect |
| 38. #11745157 | C22 | semidirect |
| 39. #11745156 | C22 | semidirect |
| 40. C4⋊#6597 | C22 | semidirect |
| 102. D116 | SD16 | semidirect |
| 139. C4×SD16 | D29 | semidirect |
| 161. C4×Q8 | C2×D29 | semidirect |
| 167. #106 | C2×D29 | semidirect |
| 169. #103 | C2×D29 | semidirect |
| 176. C4×C8 | C2×D29 | semidirect |
| 177. C29 | #3295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271873 | 2 |
| D4×D116 | 2 |
| #14271510 | 2 |
| #14271483 | 2 |
| #14271453 | 2 |
| #14271395 | 2 |
| #14271363 | 2 |
| #14271312 | 2 |
| C8×D116 | 2 |
| #102×D29 | 2 |
| C4×SD16×C29 | 2 |
| #3295 | 29 |