Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 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. #14558335 | C2 | semidirect |
| 2. #14557970 | C2 | semidirect |
| 3. #14557968 | C2 | semidirect |
| 4. #14557966 | C2 | semidirect |
| 5. C2×D592 | C2 | semidirect |
| 6. D16×D37 | C2 | semidirect |
| 7. #14557949 | C2 | semidirect |
| 8. C37×#508 | C2 | semidirect |
| 12. #11924559 | C22 | semidirect |
| 13. C2×D296 | C22 | semidirect |
| 14. D8×D37 | C22 | semidirect |
| 16. #11924479 | C22 | semidirect |
| 17. D592 | C22 | semidirect |
| 18. D592 | C22 | semidirect |
| 19. #11924477 | C22 | semidirect |
| 20. #11924476 | C22 | semidirect |
| 21. #11924475 | C22 | semidirect |
| 22. C16×D37 | C22 | semidirect |
| 23. #135×C37 | C22 | semidirect |
| 24. Q32×C37 | C22 | semidirect |
| 25. SD32×C37 | C22 | semidirect |
| 26. D16×C37 | C22 | semidirect |
| 27. C2×C16×C37 | C22 | semidirect |
| 89. #508 | D37 | semidirect |
| 93. C37 | #3415 | semidirect |
| 98. #135 | C2×D37 | semidirect |
| 102. Q32 | C2×D37 | semidirect |
| 104. SD32 | C2×D37 | semidirect |
| 108. D16 | C2×D37 | semidirect |
| 112. C2×C16 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558335 | 2 |
| #14557970 | 2 |
| #14557968 | 2 |
| #14557966 | 2 |
| C2×D592 | 2 |
| D16×D37 | 2 |
| #14557949 | 2 |
| C37×#508 | 2 |
| #3415 | 37 |