Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
778 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 200 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. D37⋊#131 | C2 | semidirect |
| 2. #14558602 | C2 | semidirect |
| 3. #14558525 | C2 | semidirect |
| 4. #14558524 | C2 | semidirect |
| 5. #14558523 | C2 | semidirect |
| 6. C2×#11924598 | C2 | semidirect |
| 10. D37⋊M16 | C22 | semidirect |
| 11. C2×D37⋊C8 | C22 | semidirect |
| 14. #11924615 | C22 | semidirect |
| 15. C2×C4⋊#3866 | C22 | semidirect |
| 16. #11924599 | C22 | semidirect |
| 17. #11924599 | C22 | semidirect |
| 18. #11924598 | C22 | semidirect |
| 19. #11924598 | C22 | semidirect |
| 20. #11924598 | C22 | semidirect |
| 22. #11924582 | C4 | semidirect |
| 23. #11924582 | C4 | semidirect |
| 25. #11924581 | C4 | semidirect |
| 31. H(5,𝔽2)×C37 | C4 | semidirect |
| 36. #41×C37 | C2×C4 | semidirect |
| 38. C2×D4×C37 | C2×C4 | semidirect |
| 42. #10596966 | C2×C4 | semidirect |
| 48. #10596964 | C2×C4 | semidirect |
| 56. D4×D37 | C2×C4 | semidirect |
| 62. #10596962 | C2×C4 | semidirect |
| 64. C2×D148 | C2×C4 | semidirect |
| 154. C37 | #2897 | semidirect |
| 160. H(5,𝔽2) | #3866 | semidirect |
| 193. #41 | C2×#3866 | semidirect |
| 210. C2×D4 | C2×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D37⋊#131 | 2 |
| #14558602 | 2 |
| #14558525 | 2 |
| #14558524 | 2 |
| #14558523 | 2 |
| C2×#11924598 | 2 |
| H(5,𝔽2)×D37 | 2 |
| #2897 | 37 |