Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 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 | C2 | D4×D268 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #443×C67 | C2 |
| socle | C2×C67 | D42 |
| hypercenter | #443 | D67 |
| hypocenter | C67 | #3290 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #443 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864210 | C2 | semidirect |
| 2. #16864208 | C2 | semidirect |
| 3. #16864198 | C2 | semidirect |
| 4. #16863780 | C2 | semidirect |
| 5. #16863672 | C2 | semidirect |
| 6. #16863667 | C2 | semidirect |
| 7. #16863659 | C2 | semidirect |
| 8. #16863575 | C2 | semidirect |
| 9. #16863570 | C2 | semidirect |
| 10. #16863514 | C2 | semidirect |
| 11. #443×C67 | C2 | semidirect |
| 12. #14524090 | C22 | semidirect |
| 16. #14524073 | C22 | semidirect |
| 19. #14524071 | C22 | semidirect |
| 26. C2×Dic268 | C22 | semidirect |
| 29. C2×#11761617 | C22 | semidirect |
| 33. #14524049 | C22 | semidirect |
| 34. #14524031 | C22 | semidirect |
| 35. #14523979 | C22 | semidirect |
| 37. #14523971 | C22 | semidirect |
| 38. #14523961 | C22 | semidirect |
| 39. #14523959 | C22 | semidirect |
| 41. #131×C67 | C22 | semidirect |
| 42. #108×C67 | C22 | semidirect |
| 43. #104×C67 | C22 | semidirect |
| 44. C4×C8×C67 | C22 | semidirect |
| 150. C67 | #3290 | semidirect |
| 161. #443 | D67 | semidirect |
| 185. #131 | C2×D67 | semidirect |
| 188. #108 | C2×D67 | semidirect |
| 191. #104 | C2×D67 | semidirect |
| 194. C4×C8 | C2×D67 | semidirect |