Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
764 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14273772 | C2 | semidirect |
| 2. C2×#14273747 | C2 | semidirect |
| 3. #16837980 | C2 | semidirect |
| 4. #16837561 | C2 | semidirect |
| 5. #16837551 | C2 | semidirect |
| 6. #16837544 | C2 | semidirect |
| 7. #16837534 | C2 | semidirect |
| 8. #16837404 | C2 | semidirect |
| 9. C2×#14273648 | C2 | semidirect |
| 10. #16837370 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C59 | C2 | semidirect |
| 22. C2×#11745672 | C22 | semidirect |
| 23. C2×#11745670 | C22 | semidirect |
| 24. C2×#11745671 | C22 | semidirect |
| 25. C2×#11745669 | C22 | semidirect |
| 26. C22×C59⋊C8 | C22 | semidirect |
| 28. #14273703 | C22 | semidirect |
| 31. #14273698 | C22 | semidirect |
| 32. C2×C4⋊Dic59 | C22 | semidirect |
| 33. #14273652 | C22 | semidirect |
| 34. #14273649 | C22 | semidirect |
| 35. #14273648 | C22 | semidirect |
| 36. #14273648 | C22 | semidirect |
| 37. (C2×D59)⋊C8 | C22 | semidirect |
| 38. (C2×D59)⋊C8 | C22 | semidirect |
| 39. C2×#41×C59 | C22 | semidirect |
| 42. C2×SD16×C59 | C22 | semidirect |
| 43. C2×D8×C59 | C22 | semidirect |
| 44. C2×M16×C59 | C22 | semidirect |
| 53. C2×D4×C59 | D4 | semidirect |
| 75. #11745685 | D4 | semidirect |
| 180. C2×AGL(1,ℤ/8) | D59 | semidirect |
| 190. C59 | #3012 | semidirect |
| 197. C2×#41 | C2×D59 | semidirect |
| 207. C2×SD16 | C2×D59 | semidirect |
| 209. C2×D8 | C2×D59 | semidirect |
| 210. C2×M16 | C2×D59 | semidirect |
| 252. C2×D4 | C22⋊D59 | semidirect |