Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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. D4×D236 | C2 | semidirect |
| 2. #16837750 | C2 | semidirect |
| 3. #16837726 | C2 | semidirect |
| 4. #16837689 | C2 | semidirect |
| 5. #16837653 | C2 | semidirect |
| 6. #16837597 | C2 | semidirect |
| 7. #16837535 | C2 | semidirect |
| 8. C4×#11745669 | C2 | semidirect |
| 9. #16837480 | C2 | semidirect |
| 10. #16837406 | C2 | semidirect |
| 11. C59×#555 | C2 | semidirect |
| 15. C2×#11745669 | C22 | semidirect |
| 16. C2×#11745664 | C22 | semidirect |
| 22. #14273660 | C22 | semidirect |
| 23. #14273658 | C22 | semidirect |
| 24. C4⋊(C59⋊C8) | C22 | semidirect |
| 25. #14273648 | C22 | semidirect |
| 28. #14273647 | C22 | semidirect |
| 29. #14273647 | C22 | semidirect |
| 30. #14273647 | C22 | semidirect |
| 31. C22⋊(C59⋊C8) | C22 | semidirect |
| 32. C4×C59⋊C8 | C22 | semidirect |
| 33. C4⋊Q8×C59 | C22 | semidirect |
| 36. #121×C59 | C22 | semidirect |
| 38. C4×D4×C59 | C22 | semidirect |
| 40. #117×C59 | C22 | semidirect |
| 141. #555 | D59 | semidirect |
| 152. C59 | #3325 | semidirect |
| 158. C4⋊Q8 | C2×D59 | semidirect |
| 164. #121 | C2×D59 | semidirect |
| 168. C4×D4 | C2×D59 | semidirect |
| 170. #117 | C2×D59 | semidirect |