Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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. #14558145 | C2 | semidirect |
| 3. #14557875 | C2 | semidirect |
| 4. #14557834 | C2 | semidirect |
| 5. #14557739 | C2 | semidirect |
| 7. #14557635 | C2 | semidirect |
| 8. C4×#10596930 | C2 | semidirect |
| 9. C37×#433 | C2 | semidirect |
| 13. #11924536 | C22 | semidirect |
| 15. #11924528 | C22 | semidirect |
| 18. C4×Dic74 | C22 | semidirect |
| 24. #11924470 | C22 | semidirect |
| 25. #11924468 | C22 | semidirect |
| 26. #11924461 | C22 | semidirect |
| 27. #11924461 | C22 | semidirect |
| 31. C4⋊C8×C37 | C22 | semidirect |
| 33. #97×C37 | C22 | semidirect |
| 34. C4×C8×C37 | C22 | semidirect |
| 111. #433 | D37 | semidirect |
| 112. C37 | #3123 | semidirect |
| 130. C4⋊C8 | C2×D37 | semidirect |
| 136. #97 | C2×D37 | semidirect |
| 137. C4×C8 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558145 | 2 |
| #14558007 | 2 |
| #14557875 | 2 |
| #14557834 | 2 |
| #14557739 | 2 |
| #14557686 | 2 |
| #14557635 | 2 |
| C4×#10596930 | 2 |
| C37×#433 | 2 |
| #3123 | 37 |