Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
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×D67 |
| commutator, socle | C22×C67 | C25 |
| Fitting | H(3,𝔽4)×C67 | C2 |
| hypercenter | H(3,𝔽4) | D67 |
| hypocenter | C67 | #3568 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864146 | C2 | semidirect |
| 2. #16864115 | C2 | semidirect |
| 3. #16864077 | C2 | semidirect |
| 4. #16864010 | C2 | semidirect |
| 5. #16863981 | C2 | semidirect |
| 6. #16863925 | C2 | semidirect |
| 7. H(3,𝔽4)×C67 | C2 | semidirect |
| 8. #14524041 | C22 | semidirect |
| 9. #14524037 | C22 | semidirect |
| 10. #14524036 | C22 | semidirect |
| 11. #14524036 | C22 | semidirect |
| 12. #14524036 | C22 | semidirect |
| 13. #14524036 | C22 | semidirect |
| 14. #14524035 | C22 | semidirect |
| 16. #14524029 | C22 | semidirect |
| 17. #14524025 | C22 | semidirect |
| 20. #14524020 | C22 | semidirect |
| 21. #14524020 | C22 | semidirect |
| 22. #14524020 | C22 | semidirect |
| 23. #14524019 | C22 | semidirect |
| 26. #14524012 | C22 | semidirect |
| 27. Q8×Dic67 | C22 | semidirect |
| 28. C4×Dic134 | C22 | semidirect |
| 31. (C22⋊D67)⋊C4 | C22 | semidirect |
| 32. #14523999 | C22 | semidirect |
| 33. #14523999 | C22 | semidirect |
| 34. C2×C22⋊Dic67 | C22 | semidirect |
| 35. C42×D67 | C22 | semidirect |
| 101. C67 | #3568 | semidirect |
| 103. H(3,𝔽4) | D67 | semidirect |