Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#10596930 | C2 | semidirect |
| 2. C2×#11924542 | C2 | semidirect |
| 3. #14558109 | C2 | semidirect |
| 5. #14557780 | C2 | semidirect |
| 6. #14557763 | C2 | semidirect |
| 7. #14557541 | C2 | semidirect |
| 8. #14557537 | C2 | semidirect |
| 9. C37×#427 | C2 | semidirect |
| 18. C2×#10596929 | C22 | semidirect |
| 19. C2×C8×D37 | C22 | semidirect |
| 25. #11924516 | C22 | semidirect |
| 28. #11924459 | C22 | semidirect |
| 33. #107×C37 | C22 | semidirect |
| 34. #106×C37 | C22 | semidirect |
| 53. C2×C8×C37 | D4 | semidirect |
| 127. #427 | D37 | semidirect |
| 130. C37 | #3057 | semidirect |
| 152. #107 | C2×D37 | semidirect |
| 153. #106 | C2×D37 | semidirect |
| 180. C2×C8 | D148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596930 | 2 |
| C2×#11924542 | 2 |
| #14558109 | 2 |
| #14558102 | 2 |
| #14557780 | 2 |
| #14557763 | 2 |
| #14557541 | 2 |
| #14557537 | 2 |
| C37×#427 | 2 |
| #3057 | 37 |