Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14273724 | C2 | semidirect |
| 2. #16837792 | C2 | semidirect |
| 3. #16837768 | C2 | semidirect |
| 4. #16837602 | C2 | semidirect |
| 5. #16837597 | C2 | semidirect |
| 6. #16837552 | C2 | semidirect |
| 7. #16837535 | C2 | semidirect |
| 8. #16837459 | C2 | semidirect |
| 9. C59×#529 | C2 | semidirect |
| 13. C2×#11745671 | C22 | semidirect |
| 14. C2×#11745669 | C22 | semidirect |
| 19. C4⋊(C59⋊C8) | C22 | semidirect |
| 20. #14273647 | C22 | semidirect |
| 21. #14273647 | C22 | semidirect |
| 23. #14273638 | C22 | semidirect |
| 25. #125×C59 | C22 | semidirect |
| 26. #124×C59 | C22 | semidirect |
| 30. C4×Q8×C59 | C22 | semidirect |
| 32. C4×D4×C59 | C22 | semidirect |
| 129. #529 | D59 | semidirect |
| 137. C59 | #3217 | semidirect |
| 148. #125 | C2×D59 | semidirect |
| 149. #124 | C2×D59 | semidirect |
| 153. C4×Q8 | C2×D59 | semidirect |
| 155. C4×D4 | C2×D59 | semidirect |