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×#14273752 | C2 | semidirect |
| 2. D4×D236 | C2 | semidirect |
| 3. #16837778 | C2 | semidirect |
| 4. #16837653 | C2 | semidirect |
| 5. #16837602 | C2 | semidirect |
| 6. #16837594 | C2 | semidirect |
| 7. #16837547 | C2 | semidirect |
| 8. #16837535 | C2 | semidirect |
| 9. C4×#11745671 | C2 | semidirect |
| 10. #16837480 | C2 | semidirect |
| 11. C59×#550 | C2 | semidirect |
| 16. C2×#11745671 | C22 | semidirect |
| 18. C2×#11745669 | C22 | semidirect |
| 19. C2×#11745669 | C22 | semidirect |
| 20. C2×#11745664 | C22 | semidirect |
| 26. #14273658 | C22 | semidirect |
| 27. C4⋊(C59⋊C8) | C22 | semidirect |
| 28. #14273651 | C22 | semidirect |
| 29. #14273648 | C22 | semidirect |
| 31. #14273647 | C22 | semidirect |
| 32. C22⋊(C59⋊C8) | C22 | semidirect |
| 33. C4×C59⋊C8 | C22 | semidirect |
| 34. C2×#41×C59 | C22 | semidirect |
| 36. #127×C59 | C22 | semidirect |
| 38. #121×C59 | C22 | semidirect |
| 39. C4×Q8×C59 | C22 | semidirect |
| 72. #11745671 | D4 | semidirect |
| 91. Q8×C59 | C2×D4 | semidirect |
| 120. C59⋊C8 | C2×D4 | semidirect |
| 139. C4×C59 | AGL(1,ℤ/8) | semidirect |
| 152. #550 | D59 | semidirect |
| 162. C59 | #3274 | semidirect |
| 163. C2×#41 | C2×D59 | semidirect |
| 175. #127 | C2×D59 | semidirect |
| 179. #121 | C2×D59 | semidirect |
| 181. C4×Q8 | C2×D59 | semidirect |
| 242. Q8 | D4×D59 | semidirect |
| 291. C4 | #14273752 | semidirect |