Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×C22⋊D67 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | D42×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | D42 | D67 |
| hypocenter | C67 | #3295 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ D42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864103 | C2 | semidirect |
| 2. #16863742 | C2 | semidirect |
| 3. #16863712 | C2 | semidirect |
| 4. #16863686 | C2 | semidirect |
| 5. #16863623 | C2 | semidirect |
| 6. #16863593 | C2 | semidirect |
| 7. #16863547 | C2 | semidirect |
| 8. C4×#11761616 | C2 | semidirect |
| 9. D4×C67⋊C8 | C2 | semidirect |
| 10. C2×#14523964 | C2 | semidirect |
| 13. C2×#11761616 | C22 | semidirect |
| 14. C22×C67⋊C8 | C22 | semidirect |
| 15. #14524043 | C22 | semidirect |
| 17. #14524022 | C22 | semidirect |
| 19. C4×Dic134 | C22 | semidirect |
| 21. C2×C4⋊Dic67 | C22 | semidirect |
| 22. #14523974 | C22 | semidirect |
| 23. #14523974 | C22 | semidirect |
| 24. C4⋊(C67⋊C8) | C22 | semidirect |
| 25. #14523966 | C22 | semidirect |
| 28. #14523964 | C22 | semidirect |
| 29. #14523964 | C22 | semidirect |
| 30. #14523964 | C22 | semidirect |
| 31. C22⋊(C67⋊C8) | C22 | semidirect |
| 32. C4×C67⋊C8 | C22 | semidirect |
| 90. D4×C67 | SD16 | semidirect |
| 137. C67 | #3295 | semidirect |
| 230. D4 | #11761616 | semidirect |