Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1258 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 455 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 | #3549 |
| 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. #16864138 | C2 | semidirect |
| 2. #16864108 | C2 | semidirect |
| 3. #16864028 | C2 | semidirect |
| 4. #16863964 | C2 | semidirect |
| 5. #16863961 | C2 | semidirect |
| 6. #16863945 | C2 | semidirect |
| 7. H(3,𝔽4)×C67 | C2 | semidirect |
| 8. C2×#11761629 | C22 | semidirect |
| 9. C2×#11761627 | C22 | semidirect |
| 10. C22×C22⋊D67 | C22 | semidirect |
| 11. C2×D4×D67 | C22 | semidirect |
| 12. #14524041 | C22 | semidirect |
| 13. #14524040 | C22 | semidirect |
| 15. #14524039 | C22 | semidirect |
| 16. #14524032 | C22 | semidirect |
| 17. #14524031 | C22 | semidirect |
| 18. #14524029 | C22 | semidirect |
| 19. #14524016 | C22 | semidirect |
| 20. #14524016 | C22 | semidirect |
| 21. #14524015 | C22 | semidirect |
| 22. #14524013 | C22 | semidirect |
| 23. #14524013 | C22 | semidirect |
| 24. #14524012 | C22 | semidirect |
| 25. #14524011 | C22 | semidirect |
| 26. (C22⋊D67)⋊C4 | C22 | semidirect |
| 27. #14524000 | C22 | semidirect |
| 28. #14523999 | C22 | semidirect |
| 29. C42×D67 | C22 | semidirect |
| 30. #124×C67 | C22 | semidirect |
| 31. #124×C67 | C22 | semidirect |
| 32. #120×C67 | C22 | semidirect |
| 102. C67 | #3549 | semidirect |
| 104. H(3,𝔽4) | D67 | semidirect |
| 121. #124 | C2×D67 | semidirect |
| 122. #124 | C2×D67 | semidirect |
| 130. #120 | C2×D67 | semidirect |