Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#11924564 | C2 | semidirect |
| 2. C2×#11924544 | C2 | semidirect |
| 3. #14558114 | C2 | semidirect |
| 4. #14558102 | C2 | semidirect |
| 5. #14557787 | C2 | semidirect |
| 6. #14557780 | C2 | semidirect |
| 7. #14557770 | C2 | semidirect |
| 8. #14557763 | C2 | semidirect |
| 9. #14557527 | C2 | semidirect |
| 10. C2×#11924456 | C2 | semidirect |
| 11. C37×#428 | C2 | semidirect |
| 19. C2×#10596929 | C22 | semidirect |
| 21. C2×C8×D37 | C22 | semidirect |
| 25. #11924516 | C22 | semidirect |
| 29. #11924511 | C22 | semidirect |
| 32. #11924459 | C22 | semidirect |
| 33. #11924459 | C22 | semidirect |
| 36. #11924456 | C22 | semidirect |
| 37. #11924456 | C22 | semidirect |
| 41. #107×C37 | C22 | semidirect |
| 42. #106×C37 | C22 | semidirect |
| 65. M16×C37 | D4 | semidirect |
| 160. #428 | D37 | semidirect |
| 163. C37 | #3062 | semidirect |
| 187. #107 | C2×D37 | semidirect |
| 188. #106 | C2×D37 | semidirect |
| 220. M16 | D148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924564 | 2 |
| C2×#11924544 | 2 |
| #14558114 | 2 |
| #14558102 | 2 |
| #14557787 | 2 |
| #14557780 | 2 |
| #14557770 | 2 |
| #14557763 | 2 |
| #14557527 | 2 |
| C2×#11924456 | 2 |
| C37×#428 | 2 |
| #3062 | 37 |