Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #14558240 | C2 | semidirect |
| 3. #14557880 | C2 | semidirect |
| 4. #14557852 | C2 | semidirect |
| 5. #14557824 | C2 | semidirect |
| 6. #14557762 | C2 | semidirect |
| 7. #14557734 | C2 | semidirect |
| 8. #14557686 | C2 | semidirect |
| 9. C4×#10596930 | C2 | semidirect |
| 10. C2×#11924458 | C2 | semidirect |
| 11. C8×D4×C37 | C2 | semidirect |
| 15. C2×#10596930 | C22 | semidirect |
| 16. #11924536 | C22 | semidirect |
| 19. #11924515 | C22 | semidirect |
| 24. C4×Dic74 | C22 | semidirect |
| 27. C2×C4⋊Dic37 | C22 | semidirect |
| 28. #11924468 | C22 | semidirect |
| 29. #11924468 | C22 | semidirect |
| 30. #11924461 | C22 | semidirect |
| 33. #11924458 | C22 | semidirect |
| 34. #11924458 | C22 | semidirect |
| 35. #11924458 | C22 | semidirect |
| 36. C22×C8×C37 | C22 | semidirect |
| 38. C4⋊C8×C37 | C22 | semidirect |
| 39. C22⋊C8×C37 | C22 | semidirect |
| 40. C4×C8×C37 | C22 | semidirect |
| 83. D4×C37 | SD16 | semidirect |
| 146. C8×D4 | D37 | semidirect |
| 148. C37 | #3295 | semidirect |
| 153. C22×C8 | C2×D37 | semidirect |
| 169. C4⋊C8 | C2×D37 | semidirect |
| 176. C22⋊C8 | C2×D37 | semidirect |
| 177. C4×C8 | C2×D37 | semidirect |
| 231. D4 | #10596930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558240 | 2 |
| D4×D148 | 2 |
| #14557880 | 2 |
| #14557852 | 2 |
| #14557824 | 2 |
| #14557762 | 2 |
| #14557734 | 2 |
| #14557686 | 2 |
| C4×#10596930 | 2 |
| C2×#11924458 | 2 |
| C8×D4×C37 | 2 |
| #3295 | 37 |