Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 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×#14273753 | C2 | semidirect |
| 2. C2×M16×D59 | C2 | semidirect |
| 3. #16837914 | C2 | semidirect |
| 4. C2×#14273698 | C2 | semidirect |
| 5. #16837654 | C2 | semidirect |
| 6. #16837647 | C2 | semidirect |
| 7. #16837637 | C2 | semidirect |
| 8. #16837630 | C2 | semidirect |
| 9. #16837445 | C2 | semidirect |
| 10. #16837404 | C2 | semidirect |
| 11. C59×#418 | C2 | semidirect |
| 16. C2×#11745670 | C22 | semidirect |
| 17. C2×#11745669 | C22 | semidirect |
| 19. C2×#11745659 | C22 | semidirect |
| 21. C2×C8×D59 | C22 | semidirect |
| 23. #14273707 | C22 | semidirect |
| 24. #14273707 | C22 | semidirect |
| 25. #14273702 | C22 | semidirect |
| 26. #14273702 | C22 | semidirect |
| 36. #14273660 | C22 | semidirect |
| 37. #14273658 | C22 | semidirect |
| 38. #14273652 | C22 | semidirect |
| 39. #14273649 | C22 | semidirect |
| 43. #102×C59 | C22 | semidirect |
| 44. #102×C59 | C22 | semidirect |
| 89. #11745664 | D4 | semidirect |
| 136. C59⋊C8 | C2×D4 | semidirect |
| 154. C2×D59 | AGL(1,ℤ/8) | semidirect |
| 182. #418 | D59 | semidirect |
| 184. C59 | #3055 | semidirect |
| 216. #102 | C2×D59 | semidirect |
| 217. #102 | C2×D59 | semidirect |