Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 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. #14558164 | C2 | semidirect |
| 3. #14557896 | C2 | semidirect |
| 4. #14557891 | C2 | semidirect |
| 5. #14557886 | C2 | semidirect |
| 6. #14557878 | C2 | semidirect |
| 7. #14557538 | C2 | semidirect |
| 8. #14557532 | C2 | semidirect |
| 9. #14557530 | C2 | semidirect |
| 10. #14557488 | C2 | semidirect |
| 11. C2×#102×C37 | C2 | semidirect |
| 15. #11924535 | C22 | semidirect |
| 18. #11924527 | C22 | semidirect |
| 26. #11924461 | C22 | semidirect |
| 27. #11924461 | C22 | semidirect |
| 28. #11924459 | C22 | semidirect |
| 29. #11924458 | C22 | semidirect |
| 30. #11924458 | C22 | semidirect |
| 33. #11924456 | C22 | semidirect |
| 34. #11924446 | C22 | semidirect |
| 35. C8×Dic37 | C22 | semidirect |
| 145. C2×#102 | D37 | semidirect |
| 147. C37 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558164 | 2 |
| #14558100 | 2 |
| #14557896 | 2 |
| #14557891 | 2 |
| #14557886 | 2 |
| #14557878 | 2 |
| #14557538 | 2 |
| #14557532 | 2 |
| #14557530 | 2 |
| #14557488 | 2 |
| C2×#102×C37 | 2 |
| #3136 | 37 |