Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
466 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 145 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. #14558331 | C2 | semidirect |
| 2. C2×#11924564 | C2 | semidirect |
| 3. C2×#11924561 | C2 | semidirect |
| 4. #14557803 | C2 | semidirect |
| 5. #14557796 | C2 | semidirect |
| 6. #14557582 | C2 | semidirect |
| 7. #14557515 | C2 | semidirect |
| 8. C2×#11924452 | C2 | semidirect |
| 9. C37×#568 | C2 | semidirect |
| 13. #11924566 | C22 | semidirect |
| 19. #11924561 | C22 | semidirect |
| 21. C2×#10596930 | C22 | semidirect |
| 23. C2×D296 | C22 | semidirect |
| 27. #11924472 | C22 | semidirect |
| 28. #11924454 | C22 | semidirect |
| 29. #11924452 | C22 | semidirect |
| 30. #11924452 | C22 | semidirect |
| 33. #131×C37 | C22 | semidirect |
| 151. #568 | D37 | semidirect |
| 157. C37 | #3068 | semidirect |
| 175. #131 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558331 | 2 |
| C2×#11924564 | 2 |
| C2×#11924561 | 2 |
| #14557803 | 2 |
| #14557796 | 2 |
| #14557582 | 2 |
| #14557515 | 2 |
| C2×#11924452 | 2 |
| C37×#568 | 2 |
| #3068 | 37 |