Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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. #16837971 | C2 | semidirect |
| 2. #16837789 | C2 | semidirect |
| 3. #16837778 | C2 | semidirect |
| 4. #16837768 | C2 | semidirect |
| 5. #16837759 | C2 | semidirect |
| 6. #16837617 | C2 | semidirect |
| 7. #16837597 | C2 | semidirect |
| 8. #16837545 | C2 | semidirect |
| 9. #16837535 | C2 | semidirect |
| 10. #16837463 | C2 | semidirect |
| 11. C59×#540 | C2 | semidirect |
| 14. C2×#11745670 | C22 | semidirect |
| 17. C2×#11745669 | C22 | semidirect |
| 24. C4⋊(C59⋊C8) | C22 | semidirect |
| 25. #14273650 | C22 | semidirect |
| 28. #14273647 | C22 | semidirect |
| 30. #14273638 | C22 | semidirect |
| 31. C4×C59⋊C8 | C22 | semidirect |
| 32. #127×C59 | C22 | semidirect |
| 33. #125×C59 | C22 | semidirect |
| 37. C4×D4×C59 | C22 | semidirect |
| 129. #540 | D59 | semidirect |
| 140. C59 | #3220 | semidirect |
| 149. #127 | C2×D59 | semidirect |
| 150. #125 | C2×D59 | semidirect |
| 158. C4×D4 | C2×D59 | semidirect |