Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
958 conjugacy classes of subgroups; only the 449 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 449 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D59 |
| commutator, socle | C22×C59 | C25 |
| Fitting | C59×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D59 |
| hypocenter | C59 | #3568 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838152 | C2 | semidirect |
| 2. #16838121 | C2 | semidirect |
| 3. #16838083 | C2 | semidirect |
| 4. #16838016 | C2 | semidirect |
| 5. #16837987 | C2 | semidirect |
| 6. #16837931 | C2 | semidirect |
| 7. C59×H(3,𝔽4) | C2 | semidirect |
| 8. #14273725 | C22 | semidirect |
| 9. #14273721 | C22 | semidirect |
| 10. #14273720 | C22 | semidirect |
| 11. #14273720 | C22 | semidirect |
| 12. #14273720 | C22 | semidirect |
| 13. #14273720 | C22 | semidirect |
| 14. #14273719 | C22 | semidirect |
| 16. #14273713 | C22 | semidirect |
| 17. #14273709 | C22 | semidirect |
| 20. #14273704 | C22 | semidirect |
| 21. #14273704 | C22 | semidirect |
| 22. #14273704 | C22 | semidirect |
| 23. #14273703 | C22 | semidirect |
| 26. #14273696 | C22 | semidirect |
| 27. Q8×Dic59 | C22 | semidirect |
| 28. C4×Dic118 | C22 | semidirect |
| 31. (C22⋊D59)⋊C4 | C22 | semidirect |
| 32. #14273683 | C22 | semidirect |
| 33. #14273683 | C22 | semidirect |
| 34. C2×C22⋊Dic59 | C22 | semidirect |
| 35. C42×D59 | C22 | semidirect |
| 102. H(3,𝔽4) | D59 | semidirect |
| 108. C59 | #3568 | semidirect |