Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
546 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 546 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. C22×#11745671 | C2 | semidirect |
| 3. #16837776 | C2 | semidirect |
| 4. #16837633 | C2 | semidirect |
| 5. #16837604 | C2 | semidirect |
| 6. #16837602 | C2 | semidirect |
| 7. #16837552 | C2 | semidirect |
| 8. #16837541 | C2 | semidirect |
| 9. C4×#11745671 | C2 | semidirect |
| 10. D4×C59⋊C8 | C2 | semidirect |
| 11. D4×Q8×C59 | C2 | semidirect |
| 17. C2×#11745671 | C22 | semidirect |
| 18. C2×#11745671 | C22 | semidirect |
| 19. C2×#11745671 | C22 | semidirect |
| 20. C22×C59⋊C8 | C22 | semidirect |
| 26. #14273658 | C22 | semidirect |
| 27. C4⋊(C59⋊C8) | C22 | semidirect |
| 28. #14273651 | C22 | semidirect |
| 29. #14273651 | C22 | semidirect |
| 31. #14273647 | C22 | semidirect |
| 32. C22⋊(C59⋊C8) | C22 | semidirect |
| 33. C4×C59⋊C8 | C22 | semidirect |
| 34. C22×Q8×C59 | C22 | semidirect |
| 36. C4⋊Q8×C59 | C22 | semidirect |
| 38. C22⋊Q8×C59 | C22 | semidirect |
| 39. C4×Q8×C59 | C22 | semidirect |
| 75. #11745671 | D4 | direct (N × H) |
| 93. Q8×C59 | C2×D4 | semidirect |
| 94. D4×C59 | SD16 | semidirect |
| 117. C59⋊C8 | C2×D4 | semidirect |
| 120. C22×C59 | C2×SD16 | semidirect |
| 134. C4×C59 | C2×SD16 | semidirect |
| 146. D4×Q8 | D59 | semidirect |
| 156. C59 | D4×SD16 | semidirect |
| 157. C22×Q8 | C2×D59 | semidirect |
| 168. C4⋊Q8 | C2×D59 | semidirect |
| 171. C22⋊Q8 | C2×D59 | semidirect |
| 175. C4×Q8 | C2×D59 | semidirect |
| 238. Q8 | D4×D59 | semidirect |
| 247. D4 | #11745671 | direct (N × H) |
| 272. C22 | C2×#11745671 | semidirect |
| 280. C4 | C2×#11745671 | semidirect |