Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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×#11924558 | C2 | semidirect |
| 2. #14557974 | C2 | semidirect |
| 3. #14557973 | C2 | semidirect |
| 4. #14557969 | C2 | semidirect |
| 5. #14557968 | C2 | semidirect |
| 6. #14557963 | C2 | semidirect |
| 7. C2×#11924476 | C2 | semidirect |
| 8. C2×#135×C37 | C2 | semidirect |
| 13. #11924558 | C22 | semidirect |
| 14. C2×Dic148 | C22 | semidirect |
| 16. C2×D296 | C22 | semidirect |
| 17. #11924482 | C22 | semidirect |
| 18. #11924480 | C22 | semidirect |
| 19. #11924479 | C22 | semidirect |
| 20. #11924477 | C22 | semidirect |
| 21. #11924476 | C22 | semidirect |
| 22. #11924476 | C22 | semidirect |
| 23. C2×#10596925 | C22 | semidirect |
| 28. #135×C37 | C22 | semidirect |
| 29. C2×Q16×C37 | C22 | semidirect |
| 31. C2×D8×C37 | C22 | semidirect |
| 122. C2×#135 | D37 | semidirect |
| 129. C37 | #3414 | semidirect |
| 139. #135 | C2×D37 | semidirect |
| 141. C2×Q16 | C2×D37 | semidirect |
| 145. C2×D8 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924558 | 2 |
| #14557974 | 2 |
| #14557973 | 2 |
| #14557969 | 2 |
| #14557968 | 2 |
| #14557963 | 2 |
| C2×#11924476 | 2 |
| C2×#135×C37 | 2 |
| #3414 | 37 |