Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
738 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 198 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. #14558612 | C2 | semidirect |
| 2. #41×#3866 | C2 | semidirect |
| 3. #14558531 | C2 | semidirect |
| 4. #14558530 | C2 | semidirect |
| 5. D37⋊#104 | C2 | semidirect |
| 6. C2×#11924600 | C2 | semidirect |
| 10. C2×#10596953 | C22 | semidirect |
| 11. D37⋊M16 | C22 | semidirect |
| 14. #11924615 | C22 | semidirect |
| 15. C2×C4×#3866 | C22 | semidirect |
| 16. #11924601 | C22 | semidirect |
| 17. #11924601 | C22 | semidirect |
| 18. #11924600 | C22 | semidirect |
| 19. #11924600 | C22 | semidirect |
| 20. #11924600 | C22 | semidirect |
| 22. #11924583 | C4 | semidirect |
| 23. #11924583 | C4 | semidirect |
| 25. #11924581 | C4 | semidirect |
| 31. H(5,𝔽2)×C37 | C4 | semidirect |
| 35. #41×C37 | C2×C4 | semidirect |
| 37. C2×D4×C37 | C2×C4 | semidirect |
| 44. Q8×D37 | C2×C4 | semidirect |
| 52. #10596964 | C2×C4 | semidirect |
| 57. D4×D37 | C2×C4 | semidirect |
| 62. #10596962 | C2×C4 | semidirect |
| 66. C2×Dic74 | C2×C4 | semidirect |
| 147. C37 | #2901 | semidirect |
| 153. H(5,𝔽2) | #3866 | semidirect |
| 189. #41 | C2×#3866 | semidirect |
| 202. C2×D4 | C2×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558612 | 2 |
| #41×#3866 | 2 |
| #14558531 | 2 |
| #14558530 | 2 |
| D37⋊#104 | 2 |
| C2×#11924600 | 2 |
| #14558368 | 2 |
| #2901 | 37 |