Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1160 conjugacy classes of subgroups; only the 471 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 471 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 | #543×C67 | C2 |
| hypercenter | #543 | D67 |
| hypocenter | C67 | #3459 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #543 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16863995 | C2 | semidirect |
| 2. #16863986 | C2 | semidirect |
| 3. #16863958 | C2 | semidirect |
| 4. #16863932 | C2 | semidirect |
| 5. #16863909 | C2 | semidirect |
| 6. C2×(C22⋊D67)⋊C4 | C2 | semidirect |
| 7. #543×C67 | C2 | semidirect |
| 8. C2×#11761629 | C22 | semidirect |
| 11. C22×C4×D67 | C22 | semidirect |
| 12. #14524038 | C22 | semidirect |
| 13. #14524034 | C22 | semidirect |
| 14. #14524032 | C22 | semidirect |
| 15. #14524028 | C22 | semidirect |
| 16. #14524027 | C22 | semidirect |
| 17. #14524019 | C22 | semidirect |
| 18. #14524018 | C22 | semidirect |
| 21. #14524013 | C22 | semidirect |
| 22. Q8×Dic67 | C22 | semidirect |
| 23. #14524005 | C22 | semidirect |
| 24. (C22⋊D67)⋊C4 | C22 | semidirect |
| 25. (C22⋊D67)⋊C4 | C22 | semidirect |
| 26. #14524001 | C22 | semidirect |
| 27. C2×Dic67⋊C4 | C22 | semidirect |
| 28. C2×(C2×D67)⋊C4 | C22 | semidirect |
| 29. C2×C4×Dic67 | C22 | semidirect |
| 30. C22⋊Q8×C67 | C22 | semidirect |
| 31. C22⋊Q8×C67 | C22 | semidirect |
| 64. C23×C67 | #41 | semidirect |
| 107. C67 | #3459 | semidirect |
| 108. #543 | D67 | semidirect |
| 125. C22⋊Q8 | C2×D67 | semidirect |
| 126. C22⋊Q8 | C2×D67 | semidirect |
| 175. C23 | #11761629 | semidirect |