Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 149 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. #14558111 | C2 | semidirect |
| 3. #14558097 | C2 | semidirect |
| 4. #14557786 | C2 | semidirect |
| 5. #14557779 | C2 | semidirect |
| 6. #14557769 | C2 | semidirect |
| 7. #14557762 | C2 | semidirect |
| 8. #14557575 | C2 | semidirect |
| 9. #14557530 | C2 | semidirect |
| 10. C2×#11924458 | C2 | semidirect |
| 11. C2×#131×C37 | C2 | semidirect |
| 19. #11924515 | C22 | semidirect |
| 23. #11924510 | C22 | semidirect |
| 29. #11924470 | C22 | semidirect |
| 30. #11924468 | C22 | semidirect |
| 31. #11924461 | C22 | semidirect |
| 32. #11924461 | C22 | semidirect |
| 35. #11924458 | C22 | semidirect |
| 36. #11924458 | C22 | semidirect |
| 40. C2×M16×C37 | C22 | semidirect |
| 42. C22×C8×C37 | C22 | semidirect |
| 66. M16×C37 | D4 | semidirect |
| 153. C2×#131 | D37 | semidirect |
| 163. C37 | #3062 | semidirect |
| 172. C2×M16 | C2×D37 | semidirect |
| 174. C22×C8 | C2×D37 | semidirect |
| 220. M16 | C22⋊D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924564 | 2 |
| #14558111 | 2 |
| #14558097 | 2 |
| #14557786 | 2 |
| #14557779 | 2 |
| #14557769 | 2 |
| #14557762 | 2 |
| #14557575 | 2 |
| #14557530 | 2 |
| C2×#11924458 | 2 |
| C2×#131×C37 | 2 |
| #3062 | 37 |