Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16864031 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #495×C67 | C2 |
| socle | C2×C67 | D42 |
| hypercenter | #495 | D67 |
| hypocenter | C67 | #3290 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #495 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864209 | C2 | semidirect |
| 2. #16864202 | C2 | semidirect |
| 3. #16864197 | C2 | semidirect |
| 4. #16863668 | C2 | semidirect |
| 5. #16863663 | C2 | semidirect |
| 6. #16863656 | C2 | semidirect |
| 7. #16863573 | C2 | semidirect |
| 8. #16863568 | C2 | semidirect |
| 9. #16863514 | C2 | semidirect |
| 10. #16863514 | C2 | semidirect |
| 11. #495×C67 | C2 | semidirect |
| 12. #14524091 | C22 | semidirect |
| 16. #14524074 | C22 | semidirect |
| 20. #14524069 | C22 | semidirect |
| 31. #14524049 | C22 | semidirect |
| 32. #14524049 | C22 | semidirect |
| 33. #14523979 | C22 | semidirect |
| 34. #14523979 | C22 | semidirect |
| 36. #14523971 | C22 | semidirect |
| 37. #14523971 | C22 | semidirect |
| 38. #14523962 | C22 | semidirect |
| 39. #14523960 | C22 | semidirect |
| 40. C2×Q16×C67 | C22 | semidirect |
| 41. C2×SD16×C67 | C22 | semidirect |
| 43. #124×C67 | C22 | semidirect |
| 44. C4×C8×C67 | C22 | semidirect |
| 150. C67 | #3290 | semidirect |
| 154. #495 | D67 | semidirect |
| 178. C2×Q16 | C2×D67 | semidirect |
| 180. C2×SD16 | C2×D67 | semidirect |
| 186. #124 | C2×D67 | semidirect |
| 194. C4×C8 | C2×D67 | semidirect |