Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14273754 | C2 | semidirect |
| 2. #16838074 | C2 | semidirect |
| 3. D4×D236 | C2 | semidirect |
| 4. #16837779 | C2 | semidirect |
| 5. #16837656 | C2 | semidirect |
| 6. #16837602 | C2 | semidirect |
| 7. #16837597 | C2 | semidirect |
| 8. #16837550 | C2 | semidirect |
| 9. #16837537 | C2 | semidirect |
| 10. #16837481 | C2 | semidirect |
| 11. C4×SD16×C59 | C2 | semidirect |
| 12. C2×#11745689 | C22 | semidirect |
| 16. C2×#11745671 | C22 | semidirect |
| 17. C2×D472 | C22 | semidirect |
| 18. C2×D472 | C22 | semidirect |
| 20. C2×#11745659 | C22 | semidirect |
| 23. #14273724 | C22 | semidirect |
| 26. #14273702 | C22 | semidirect |
| 31. C4⋊(C59⋊C8) | C22 | semidirect |
| 32. #14273647 | C22 | semidirect |
| 33. #14273647 | C22 | semidirect |
| 34. (C2×D59)⋊C8 | C22 | semidirect |
| 36. C4×Q8×C59 | C22 | semidirect |
| 38. #106×C59 | C22 | semidirect |
| 39. #103×C59 | C22 | semidirect |
| 41. C4×C8×C59 | C22 | semidirect |
| 64. SD16×C59 | D4 | semidirect |
| 91. Q8×C59 | C2×D4 | semidirect |
| 119. C8×C59 | C2×D4 | semidirect |
| 139. C4×C59 | AGL(1,ℤ/8) | semidirect |
| 160. C4×SD16 | D59 | semidirect |
| 162. C59 | #3274 | semidirect |
| 181. C4×Q8 | C2×D59 | semidirect |
| 185. #106 | C2×D59 | semidirect |
| 187. #103 | C2×D59 | semidirect |
| 192. C4×C8 | C2×D59 | semidirect |
| 216. SD16 | D236 | semidirect |
| 242. Q8 | C2×D236 | semidirect |
| 271. C8 | C2×D236 | semidirect |
| 291. C4 | #14273754 | semidirect |