Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#10596942 | C2 | semidirect |
| 2. C22×#10596930 | C2 | semidirect |
| 4. C2×#11924525 | C2 | semidirect |
| 5. C2×#11924523 | C2 | semidirect |
| 6. #14557914 | C2 | direct (N × H) |
| 7. C2×C8×Dic37 | C2 | semidirect |
| 8. C22×SD16×C37 | C2 | semidirect |
| 12. C2×#10596942 | C22 | semidirect |
| 14. C2×#10596930 | C22 | semidirect |
| 19. #11924525 | C22 | semidirect |
| 21. #11924523 | C22 | semidirect |
| 25. C8×Dic37 | C22 | semidirect |
| 29. C2×SD16×C37 | C22 | semidirect |
| 113. C2×C37 | #495 | semidirect |
| 119. C22×SD16 | D37 | semidirect |
| 125. C37 | C2×#495 | semidirect |
| 135. C2×SD16 | C2×D37 | semidirect |
| 230. C2 | #14557914 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596942 | 2 |
| C22×#10596930 | 2 |
| C22×#10596939 | 2 |
| C2×#11924525 | 2 |
| C2×#11924523 | 2 |
| #14557914 | 2 |
| C2×C8×Dic37 | 2 |
| C22×SD16×C37 | 2 |
| C2×#495 | 37 |