Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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 | #432×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #432 | D67 |
| hypocenter | C67 | #3114 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #432 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16863930 | C2 | semidirect |
| 2. C2×C4×D268 | C2 | semidirect |
| 3. #16863727 | C2 | semidirect |
| 4. #16863710 | C2 | semidirect |
| 5. #16863697 | C2 | semidirect |
| 6. #16863612 | C2 | semidirect |
| 7. #16863549 | C2 | semidirect |
| 9. #16863509 | C2 | semidirect |
| 10. #16863498 | C2 | semidirect |
| 11. #432×C67 | C2 | semidirect |
| 17. #14524035 | C22 | semidirect |
| 18. #14524031 | C22 | semidirect |
| 22. C4×Dic134 | C22 | semidirect |
| 27. C4×D268 | C22 | semidirect |
| 32. #14523977 | C22 | semidirect |
| 33. #14523975 | C22 | semidirect |
| 34. #14523968 | C22 | semidirect |
| 37. #14523965 | C22 | semidirect |
| 39. C4⋊C8×C67 | C22 | semidirect |
| 42. #97×C67 | C22 | semidirect |
| 141. C67 | #3114 | semidirect |
| 152. #432 | D67 | semidirect |
| 176. C4⋊C8 | C2×D67 | semidirect |
| 183. #97 | C2×D67 | semidirect |