Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
596 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#11924560 | C2 | semidirect |
| 2. C2×#11924555 | C2 | semidirect |
| 3. C2×D8×D37 | C2 | semidirect |
| 4. #14558096 | C2 | semidirect |
| 5. #14557921 | C2 | semidirect |
| 6. #14557920 | C2 | semidirect |
| 7. #14557917 | C2 | semidirect |
| 8. #14557916 | C2 | semidirect |
| 9. #14557908 | C2 | semidirect |
| 10. #14557487 | C2 | semidirect |
| 11. C37×#493 | C2 | semidirect |
| 16. C2×Dic148 | C22 | semidirect |
| 17. C2×#10596930 | C22 | semidirect |
| 18. C2×#10596940 | C22 | semidirect |
| 19. C2×#10596940 | C22 | semidirect |
| 22. C2×#10596939 | C22 | semidirect |
| 26. #11924532 | C22 | semidirect |
| 27. #11924524 | C22 | semidirect |
| 28. #11924523 | C22 | semidirect |
| 32. #11924447 | C22 | semidirect |
| 33. #11924446 | C22 | semidirect |
| 34. C8×Dic37 | C22 | semidirect |
| 36. C2×D8×C37 | C22 | semidirect |
| 37. C2×D8×C37 | C22 | semidirect |
| 38. #127×C37 | C22 | semidirect |
| 39. C4×C8×C37 | C22 | semidirect |
| 75. #10596929 | D4 | semidirect |
| 76. C8×D37 | D4 | semidirect |
| 139. #493 | D37 | semidirect |
| 141. C37 | #3155 | semidirect |
| 155. C2×D8 | C2×D37 | semidirect |
| 156. C2×D8 | C2×D37 | semidirect |
| 160. #127 | C2×D37 | semidirect |
| 169. C4×C8 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924560 | 2 |
| C2×#11924555 | 2 |
| C2×D8×D37 | 2 |
| #14558096 | 2 |
| #14557921 | 2 |
| #14557920 | 2 |
| #14557917 | 2 |
| #14557916 | 2 |
| #14557908 | 2 |
| #14557487 | 2 |
| C37×#493 | 2 |
| #3155 | 37 |