Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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×D8×D37 | C2 | semidirect |
| 2. C2×#11924542 | C2 | semidirect |
| 3. #14558099 | C2 | semidirect |
| 4. #14557785 | C2 | semidirect |
| 5. #14557784 | C2 | semidirect |
| 6. #14557770 | C2 | semidirect |
| 7. #14557769 | C2 | semidirect |
| 8. #14557766 | C2 | semidirect |
| 9. #14557570 | C2 | semidirect |
| 10. #14557536 | C2 | semidirect |
| 11. C37×#466 | C2 | semidirect |
| 18. C2×#10596934 | C22 | semidirect |
| 20. C2×#10596929 | C22 | semidirect |
| 22. C2×C8×D37 | C22 | semidirect |
| 25. #11924511 | C22 | semidirect |
| 26. #11924510 | C22 | semidirect |
| 27. #11924507 | C22 | semidirect |
| 31. #11924470 | C22 | semidirect |
| 32. #11924467 | C22 | semidirect |
| 33. #11924458 | C22 | semidirect |
| 34. #11924457 | C22 | semidirect |
| 35. #11924456 | C22 | semidirect |
| 37. C22×C8×C37 | C22 | semidirect |
| 38. #121×C37 | C22 | semidirect |
| 39. #107×C37 | C22 | semidirect |
| 40. #102×C37 | C22 | semidirect |
| 80. C8×D37 | D4 | semidirect |
| 159. #466 | D37 | semidirect |
| 162. C37 | #3058 | semidirect |
| 175. C22×C8 | C2×D37 | semidirect |
| 181. #121 | C2×D37 | semidirect |
| 186. #107 | C2×D37 | semidirect |
| 191. #102 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D37 | 2 |
| C2×#11924542 | 2 |
| #14558099 | 2 |
| #14557785 | 2 |
| #14557784 | 2 |
| #14557770 | 2 |
| #14557769 | 2 |
| #14557766 | 2 |
| #14557570 | 2 |
| #14557536 | 2 |
| C37×#466 | 2 |
| #3058 | 37 |