Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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. #135×D37 | C2 | semidirect |
| 2. #14557975 | C2 | semidirect |
| 3. #14557972 | C2 | semidirect |
| 4. #14557970 | C2 | semidirect |
| 5. #14557967 | C2 | semidirect |
| 6. #14557965 | C2 | semidirect |
| 7. #14557963 | C2 | semidirect |
| 8. C2×#11924475 | C2 | semidirect |
| 9. C37×#508 | C2 | semidirect |
| 12. #11924558 | C22 | semidirect |
| 16. Q16×D37 | C22 | semidirect |
| 18. D8×D37 | C22 | semidirect |
| 20. Dic296 | C22 | semidirect |
| 21. #11924482 | C22 | semidirect |
| 22. #11924481 | C22 | semidirect |
| 23. #11924480 | C22 | semidirect |
| 24. #11924479 | C22 | semidirect |
| 25. D592 | C22 | semidirect |
| 26. #11924477 | C22 | semidirect |
| 27. #11924475 | C22 | semidirect |
| 28. #11924475 | C22 | semidirect |
| 29. C2×#10596925 | C22 | semidirect |
| 30. #135×C37 | C22 | semidirect |
| 31. Q32×C37 | C22 | semidirect |
| 32. SD32×C37 | C22 | semidirect |
| 33. D16×C37 | C22 | semidirect |
| 34. C2×C16×C37 | C22 | semidirect |
| 111. #508 | D37 | semidirect |
| 113. C37 | #3414 | semidirect |
| 120. #135 | C2×D37 | semidirect |
| 127. Q32 | C2×D37 | semidirect |
| 131. SD32 | C2×D37 | semidirect |
| 134. D16 | C2×D37 | semidirect |
| 138. C2×C16 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D37 | 2 |
| #14557975 | 2 |
| #14557972 | 2 |
| #14557970 | 2 |
| #14557967 | 2 |
| #14557965 | 2 |
| #14557963 | 2 |
| C2×#11924475 | 2 |
| C37×#508 | 2 |
| #3414 | 37 |