Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
592 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 145 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×Q16×D37 | C2 | semidirect |
| 2. C2×SD16×D37 | C2 | semidirect |
| 4. #124×D37 | C2 | semidirect |
| 5. #14557918 | C2 | semidirect |
| 6. #14557917 | C2 | semidirect |
| 7. #14557916 | C2 | semidirect |
| 8. #14557915 | C2 | semidirect |
| 9. #14557914 | C2 | semidirect |
| 10. C4×C8×D37 | C2 | semidirect |
| 11. C37×#495 | C2 | semidirect |
| 14. C2×Dic148 | C22 | semidirect |
| 15. C2×#10596942 | C22 | semidirect |
| 17. C2×#10596930 | C22 | semidirect |
| 18. C2×#10596940 | C22 | semidirect |
| 19. C2×#10596941 | C22 | semidirect |
| 26. #11924525 | C22 | semidirect |
| 27. #11924524 | C22 | semidirect |
| 28. #11924523 | C22 | semidirect |
| 32. C4×#64436 | C22 | semidirect |
| 33. C8×Dic37 | C22 | semidirect |
| 34. C8×Dic37 | C22 | semidirect |
| 35. C2×Q16×C37 | C22 | semidirect |
| 36. C2×SD16×C37 | C22 | semidirect |
| 38. #124×C37 | C22 | semidirect |
| 39. C4×C8×C37 | C22 | semidirect |
| 126. D37 | #495 | direct (N × H) |
| 136. #495 | D37 | direct (N × H) |
| 138. C37 | C2×#495 | semidirect |
| 144. C2×Q16 | C2×D37 | semidirect |
| 149. C2×SD16 | C2×D37 | semidirect |
| 160. #124 | C2×D37 | semidirect |
| 166. C4×C8 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D37 | 2 |
| C2×SD16×D37 | 2 |
| C2×D8×D37 | 2 |
| #124×D37 | 2 |
| #14557918 | 2 |
| #14557917 | 2 |
| #14557916 | 2 |
| #14557915 | 2 |
| #14557914 | 2 |
| C4×C8×D37 | 2 |
| C37×#495 | 2 |
| C2×#495 | 37 |