Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14558338 | C2 | semidirect |
| 2. #14558335 | C2 | semidirect |
| 3. #14557910 | C2 | semidirect |
| 4. #14557804 | C2 | semidirect |
| 5. #14557803 | C2 | semidirect |
| 6. #14557702 | C2 | semidirect |
| 7. #14557651 | C2 | semidirect |
| 8. C37×#443 | C2 | semidirect |
| 9. #11924582 | C22 | semidirect |
| 11. #11924564 | C22 | semidirect |
| 13. #11924561 | C22 | semidirect |
| 18. C2×D296 | C22 | semidirect |
| 19. C2×D296 | C22 | semidirect |
| 21. #11924542 | C22 | semidirect |
| 22. #11924533 | C22 | semidirect |
| 23. #11924472 | C22 | semidirect |
| 24. #11924464 | C22 | semidirect |
| 25. #11924452 | C22 | semidirect |
| 27. #131×C37 | C22 | semidirect |
| 28. #108×C37 | C22 | semidirect |
| 29. #104×C37 | C22 | semidirect |
| 30. C4×C8×C37 | C22 | semidirect |
| 40. Q16×C37 | D4 | semidirect |
| 41. SD16×C37 | D4 | semidirect |
| 42. D8×C37 | D4 | semidirect |
| 52. Dic148 | D4 | semidirect |
| 58. D296 | D4 | semidirect |
| 60. #10596930 | D4 | semidirect |
| 111. #443 | D37 | semidirect |
| 112. C37 | #3292 | semidirect |
| 127. #131 | C2×D37 | semidirect |
| 130. #108 | C2×D37 | semidirect |
| 132. #104 | C2×D37 | semidirect |
| 134. C4×C8 | C2×D37 | semidirect |
| 145. Q16 | D148 | semidirect |
| 149. SD16 | D148 | semidirect |
| 157. D8 | D148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558338 | 2 |
| #14558335 | 2 |
| #14557910 | 2 |
| #14557804 | 2 |
| #14557803 | 2 |
| #14557702 | 2 |
| #14557651 | 2 |
| C37×#443 | 2 |
| #3292 | 37 |