Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14558329 | C2 | semidirect |
| 2. C2×#11924555 | C2 | semidirect |
| 3. #131×D37 | C2 | semidirect |
| 4. #14557809 | C2 | semidirect |
| 5. #14557808 | C2 | semidirect |
| 6. #14557800 | C2 | semidirect |
| 7. #14557795 | C2 | semidirect |
| 8. #14557794 | C2 | semidirect |
| 9. #108×D37 | C2 | semidirect |
| 10. #14557514 | C2 | semidirect |
| 11. C37×#472 | C2 | semidirect |
| 25. C2×Dic148 | C22 | semidirect |
| 26. C2×#10596940 | C22 | semidirect |
| 37. #11924472 | C22 | semidirect |
| 38. #11924471 | C22 | semidirect |
| 39. #11924454 | C22 | semidirect |
| 40. #11924454 | C22 | semidirect |
| 41. #11924453 | C22 | semidirect |
| 43. C2×D8×C37 | C22 | semidirect |
| 45. #108×C37 | C22 | semidirect |
| 46. #100×C37 | C22 | semidirect |
| 173. #472 | D37 | semidirect |
| 178. C37 | #3067 | semidirect |
| 195. C2×D8 | C2×D37 | semidirect |
| 209. #108 | C2×D37 | semidirect |
| 213. #100 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558329 | 2 |
| C2×#11924555 | 2 |
| #131×D37 | 2 |
| #14557809 | 2 |
| #14557808 | 2 |
| #14557800 | 2 |
| #14557795 | 2 |
| #14557794 | 2 |
| #108×D37 | 2 |
| #14557514 | 2 |
| C37×#472 | 2 |
| #3067 | 37 |