Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 221 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. #14558011 | C2 | semidirect |
| 3. #14557634 | C2 | semidirect |
| 4. SD16×Dic37 | C2 | semidirect |
| 5. #14557571 | C2 | semidirect |
| 6. #14557542 | C2 | semidirect |
| 8. #14557488 | C2 | semidirect |
| 12. Q8×Dic37 | C22 | semidirect |
| 20. #11924470 | C22 | semidirect |
| 21. #11924468 | C22 | semidirect |
| 22. #11924460 | C22 | semidirect |
| 24. #11924446 | C22 | semidirect |
| 25. C8×Dic37 | C22 | semidirect |
| 28. C2×SD16×C37 | C4 | semidirect |
| 35. C2×Q8×C37 | C2×C4 | semidirect |
| 44. SD16×C37 | C2×C4 | semidirect |
| 45. SD16×C37 | C2×C4 | semidirect |
| 46. C2×C8×C37 | C2×C4 | semidirect |
| 113. C37 | #2949 | semidirect |
| 116. C2×SD16 | Dic37 | semidirect |
| 139. C2×Q8 | C2×Dic37 | semidirect |
| 148. SD16 | C2×Dic37 | semidirect |
| 149. SD16 | C2×Dic37 | semidirect |
| 152. C2×C8 | C2×Dic37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558011 | 2 |
| #14558008 | 2 |
| #14557634 | 2 |
| SD16×Dic37 | 2 |
| #14557571 | 2 |
| #14557542 | 2 |
| #14557538 | 2 |
| #14557488 | 2 |
| C22×SD16×C37 | 2 |
| #2949 | 37 |