Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
5956 conjugacy classes of subgroups; only the 3203 normal subgroups are shown.
This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3203 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C24×D59 |
| commutator, socle | C2×C59 | C26 |
| Frattini | C2 | C25×D59 |
| Fitting | C59×#585 | C2 |
| hypercenter | #585 | D59 |
| hypocenter | C59 | C2×#585 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C4 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838239 | C2 | semidirect |
| 2. #16838238 | C2 | semidirect |
| 3. #16838237 | C2 | semidirect |
| 4. 2−1+4×D59 | C2 | semidirect |
| 5. H(5,𝔽2)×D59 | C2 | semidirect |
| 6. C2×#41×D59 | C2 | semidirect |
| 7. C59×#585 | C2 | semidirect |
| 8. #14273775 | C22 | semidirect |
| 9. #14273774 | C22 | semidirect |
| 10. #14273773 | C22 | semidirect |
| 11. #14273772 | C22 | semidirect |
| 12. C2×#11745689 | C22 | semidirect |
| 13. C2×#11745685 | C22 | semidirect |
| 14. C2×#11745687 | C22 | semidirect |
| 15. #41×D59 | C22 | semidirect |
| 16. #41×D59 | C22 | semidirect |
| 17. #41×D59 | C22 | semidirect |
| 18. #41×D59 | C22 | semidirect |
| 19. C2×Q8×D59 | C22 | semidirect |
| 20. C2×D4×D59 | C22 | semidirect |
| 21. C22×C4×D59 | C22 | semidirect |
| 22. 2−1+4×C59 | C22 | semidirect |
| 23. H(5,𝔽2)×C59 | C22 | semidirect |
| 24. C2×#41×C59 | C22 | semidirect |
| 26. #41×C59 | C23 | semidirect |
| 27. #41×C59 | C23 | semidirect |
| 28. C2×Q8×C59 | C23 | semidirect |
| 29. C2×D4×C59 | C23 | semidirect |
| 30. C22×C4×C59 | C23 | semidirect |
| 31. C2×C22⋊D59 | C23 | semidirect |
| 32. C22×Dic59 | C23 | semidirect |
| 33. #11745689 | C23 | semidirect |
| 34. #11745689 | C23 | semidirect |
| 36. Q8×D59 | C23 | semidirect |
| 37. #11745687 | C23 | semidirect |
| 38. #11745687 | C23 | semidirect |
| 40. D4×D59 | C23 | semidirect |
| 41. #11745685 | C23 | semidirect |
| 42. #11745685 | C23 | semidirect |
| 43. C2×D236 | C23 | semidirect |
| 46. C2×C4×D59 | C23 | semidirect |
| 47. C2×C4×D59 | C23 | semidirect |
| 48. C2×Dic118 | C23 | semidirect |
| 81. D59 | #585 | direct (N × H) |
| 85. #585 | D59 | direct (N × H) |
| 89. C59 | C2×#585 | semidirect |
| 92. 2−1+4 | C2×D59 | semidirect |
| 95. H(5,𝔽2) | C2×D59 | semidirect |
| 103. C2×#41 | C2×D59 | semidirect |
| 114. #41 | C22×D59 | semidirect |
| 115. #41 | C22×D59 | semidirect |
| 119. C2×Q8 | C22×D59 | semidirect |
| 124. C2×D4 | C22×D59 | semidirect |
| 130. C22×C4 | C22×D59 | semidirect |