Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
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. #16838204 | C2 | semidirect |
| 2. #16838203 | C2 | semidirect |
| 3. #16837840 | C2 | semidirect |
| 4. #16837839 | C2 | semidirect |
| 5. #16837836 | C2 | semidirect |
| 6. #16837833 | C2 | semidirect |
| 7. #16837832 | C2 | semidirect |
| 8. C2×#14273668 | C2 | semidirect |
| 9. D16×D59 | C2 | semidirect |
| 10. #16837820 | C2 | semidirect |
| 11. C59×#509 | C2 | semidirect |
| 18. #14273750 | C22 | semidirect |
| 19. #14273749 | C22 | semidirect |
| 20. #14273746 | C22 | semidirect |
| 21. C2×D472 | C22 | semidirect |
| 22. D8×D59 | C22 | semidirect |
| 23. D8×D59 | C22 | semidirect |
| 25. #14273673 | C22 | semidirect |
| 26. #14273672 | C22 | semidirect |
| 27. #14273671 | C22 | semidirect |
| 28. #14273670 | C22 | semidirect |
| 29. D944 | C22 | semidirect |
| 30. #14273668 | C22 | semidirect |
| 31. #14273668 | C22 | semidirect |
| 32. #14273668 | C22 | semidirect |
| 33. #14273666 | C22 | semidirect |
| 34. C2×C59⋊C16 | C22 | semidirect |
| 35. C16×D59 | C22 | semidirect |
| 36. #135×C59 | C22 | semidirect |
| 37. C2×D8×C59 | C22 | semidirect |
| 38. SD32×C59 | C22 | semidirect |
| 39. D16×C59 | C22 | semidirect |
| 40. M32×C59 | C22 | semidirect |
| 135. #509 | D59 | semidirect |
| 141. C59 | #3415 | semidirect |
| 151. #135 | C2×D59 | semidirect |
| 155. C2×D8 | C2×D59 | semidirect |
| 161. SD32 | C2×D59 | semidirect |
| 166. D16 | C2×D59 | semidirect |
| 168. M32 | C2×D59 | semidirect |