Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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×D268 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #436×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #436 | D67 |
| hypocenter | C67 | #3325 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ #436 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864111 | C2 | semidirect |
| 2. D4×D268 | C2 | semidirect |
| 3. #16863743 | C2 | semidirect |
| 4. #16863721 | C2 | semidirect |
| 5. #16863687 | C2 | semidirect |
| 6. #16863649 | C2 | semidirect |
| 7. #16863592 | C2 | semidirect |
| 8. #16863532 | C2 | semidirect |
| 9. C4×D536 | C2 | semidirect |
| 10. #16863402 | C2 | semidirect |
| 11. #436×C67 | C2 | semidirect |
| 15. C2×D536 | C22 | semidirect |
| 16. #14524043 | C22 | semidirect |
| 21. #14524017 | C22 | semidirect |
| 25. C4×D268 | C22 | semidirect |
| 26. #14524002 | C22 | semidirect |
| 28. #14523977 | C22 | semidirect |
| 29. #14523975 | C22 | semidirect |
| 32. #14523965 | C22 | semidirect |
| 33. #14523965 | C22 | semidirect |
| 34. #14523965 | C22 | semidirect |
| 35. #14523965 | C22 | semidirect |
| 36. C2×M16×C67 | C22 | semidirect |
| 38. C4⋊C8×C67 | C22 | semidirect |
| 39. C22⋊C8×C67 | C22 | semidirect |
| 40. C4×C8×C67 | C22 | semidirect |
| 141. C67 | #3325 | semidirect |
| 151. #436 | D67 | semidirect |
| 157. C2×M16 | C2×D67 | semidirect |
| 173. C4⋊C8 | C2×D67 | semidirect |
| 180. C22⋊C8 | C2×D67 | semidirect |
| 181. C4×C8 | C2×D67 | semidirect |