Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
596 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×D8×D59 | C2 | semidirect |
| 2. C2×M16×D59 | C2 | semidirect |
| 3. #121×D59 | C2 | semidirect |
| 4. #16837656 | C2 | semidirect |
| 5. #16837655 | C2 | semidirect |
| 6. #16837654 | C2 | semidirect |
| 7. #16837653 | C2 | semidirect |
| 8. #16837652 | C2 | semidirect |
| 9. #106×D59 | C2 | semidirect |
| 10. #102×D59 | C2 | semidirect |
| 11. C59×#469 | C2 | semidirect |
| 15. C2×D472 | C22 | semidirect |
| 16. C2×#11745669 | C22 | semidirect |
| 18. C2×#11745664 | C22 | semidirect |
| 19. C2×#11745659 | C22 | semidirect |
| 20. C2×#11745659 | C22 | semidirect |
| 24. #14273702 | C22 | semidirect |
| 25. #14273701 | C22 | semidirect |
| 28. #14273698 | C22 | semidirect |
| 31. #14273659 | C22 | semidirect |
| 32. #14273658 | C22 | semidirect |
| 33. #14273649 | C22 | semidirect |
| 34. #14273648 | C22 | semidirect |
| 35. #14273647 | C22 | semidirect |
| 36. C2×D8×C59 | C22 | semidirect |
| 37. C2×M16×C59 | C22 | semidirect |
| 38. #121×C59 | C22 | semidirect |
| 39. #106×C59 | C22 | semidirect |
| 40. #102×C59 | C22 | semidirect |
| 81. C8×D59 | D4 | semidirect |
| 118. C8×C59 | C2×D4 | semidirect |
| 120. C59⋊C8 | C2×D4 | semidirect |
| 150. D59 | #469 | direct (N × H) |
| 159. #469 | D59 | direct (N × H) |
| 162. C59 | C2×#469 | semidirect |
| 169. C2×D8 | C2×D59 | semidirect |
| 174. C2×M16 | C2×D59 | semidirect |
| 182. #121 | C2×D59 | semidirect |
| 187. #106 | C2×D59 | semidirect |
| 191. #102 | C2×D59 | semidirect |
| 271. C8 | D4×D59 | semidirect |