Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
584 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#14273723 | C2 | semidirect |
| 3. #41×Dic59 | C2 | semidirect |
| 4. #16837600 | C2 | semidirect |
| 5. #16837595 | C2 | semidirect |
| 6. #16837425 | C2 | semidirect |
| 7. #16837408 | C2 | semidirect |
| 8. #16837407 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C59 | C2 | semidirect |
| 13. C2×#11745671 | C22 | semidirect |
| 14. C2×#11745669 | C22 | semidirect |
| 19. Q8×Dic59 | C22 | semidirect |
| 21. D4×Dic59 | C22 | semidirect |
| 26. Dic59⋊C8 | C22 | semidirect |
| 27. #14273649 | C22 | semidirect |
| 28. #14273648 | C22 | semidirect |
| 32. C2×SD16×C59 | C22 | semidirect |
| 33. C2×D8×C59 | C22 | semidirect |
| 38. #41×C59 | D4 | semidirect |
| 83. Q8×C59 | C2×D4 | semidirect |
| 89. D4×C59 | C2×D4 | semidirect |
| 125. Dic59 | AGL(1,ℤ/8) | semidirect |
| 134. C2×AGL(1,ℤ/8) | D59 | semidirect |
| 142. C59 | #3038 | semidirect |
| 150. C2×SD16 | C2×D59 | semidirect |
| 152. C2×D8 | C2×D59 | semidirect |
| 171. #41 | C22⋊D59 | semidirect |
| 216. Q8 | C2×C22⋊D59 | semidirect |
| 227. D4 | C2×C22⋊D59 | semidirect |