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. #14271874 | C2 | semidirect |
| 3. #14271511 | C2 | semidirect |
| 4. #14271483 | C2 | semidirect |
| 5. #14271393 | C2 | semidirect |
| 6. #14271364 | C2 | semidirect |
| 7. #14271315 | C2 | semidirect |
| 8. C4×#90783 | C2 | semidirect |
| 9. #14271228 | C2 | semidirect |
| 10. #102×D29 | C2 | semidirect |
| 11. C29×#476 | C2 | semidirect |
| 14. C29×C4⋊Q8 | C22 | semidirect |
| 19. C2×#90773 | C22 | semidirect |
| 20. C2×C8×D29 | C22 | semidirect |
| 21. #11745259 | C22 | semidirect |
| 24. C4⋊C4×D29 | C22 | semidirect |
| 29. C4×Dic58 | C22 | semidirect |
| 30. C29×#106 | C22 | semidirect |
| 31. C29×C4⋊C8 | C22 | semidirect |
| 34. #11745169 | C22 | semidirect |
| 35. #11745168 | C22 | semidirect |
| 36. #11745158 | C22 | semidirect |
| 37. #11745157 | C22 | semidirect |
| 38. #11745157 | C22 | semidirect |
| 39. #11745156 | C22 | semidirect |
| 40. C4×#6597 | C22 | semidirect |
| 101. D116 | SD16 | semidirect |
| 135. #476 | D29 | semidirect |
| 153. C4⋊Q8 | C2×D29 | semidirect |
| 167. #106 | C2×D29 | semidirect |
| 168. 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 |
|---|---|
| #14271874 | 2 |
| D4×D116 | 2 |
| #14271511 | 2 |
| #14271483 | 2 |
| #14271393 | 2 |
| #14271364 | 2 |
| #14271315 | 2 |
| C4×#90783 | 2 |
| #14271228 | 2 |
| #102×D29 | 2 |
| C29×#476 | 2 |
| #3295 | 29 |