Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 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. #14558347 | C2 | semidirect |
| 2. #14558345 | C2 | semidirect |
| 3. #14558335 | C2 | semidirect |
| 4. #14557917 | C2 | semidirect |
| 5. #14557809 | C2 | semidirect |
| 6. #14557804 | C2 | semidirect |
| 7. #14557796 | C2 | semidirect |
| 8. #14557712 | C2 | semidirect |
| 9. #14557707 | C2 | semidirect |
| 10. #14557651 | C2 | semidirect |
| 11. C37×#443 | C2 | semidirect |
| 12. #11924583 | C22 | semidirect |
| 16. #11924566 | C22 | semidirect |
| 19. #11924564 | C22 | semidirect |
| 26. C2×Dic148 | C22 | semidirect |
| 29. C2×#10596930 | C22 | semidirect |
| 33. #11924542 | C22 | semidirect |
| 34. #11924524 | C22 | semidirect |
| 35. #11924472 | C22 | semidirect |
| 37. #11924464 | C22 | semidirect |
| 38. #11924454 | C22 | semidirect |
| 39. #11924452 | C22 | semidirect |
| 41. #131×C37 | C22 | semidirect |
| 42. #108×C37 | C22 | semidirect |
| 43. #104×C37 | C22 | semidirect |
| 44. C4×C8×C37 | C22 | semidirect |
| 160. #443 | D37 | semidirect |
| 161. C37 | #3290 | semidirect |
| 185. #131 | C2×D37 | semidirect |
| 188. #108 | C2×D37 | semidirect |
| 191. #104 | C2×D37 | semidirect |
| 194. C4×C8 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558347 | 2 |
| #14558345 | 2 |
| #14558335 | 2 |
| #14557917 | 2 |
| #14557809 | 2 |
| #14557804 | 2 |
| #14557796 | 2 |
| #14557712 | 2 |
| #14557707 | 2 |
| #14557651 | 2 |
| C37×#443 | 2 |
| #3290 | 37 |