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×C22⋊D67 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #578×C67 | C2 |
| socle | C2×C67 | D42 |
| hypercenter | #578 | D67 |
| hypocenter | C67 | #3290 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #578 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864204 | C2 | semidirect |
| 2. #16864198 | C2 | semidirect |
| 3. #16863781 | C2 | semidirect |
| 4. #16863668 | C2 | semidirect |
| 5. #16863666 | C2 | semidirect |
| 6. #16863661 | C2 | semidirect |
| 7. #16863572 | C2 | semidirect |
| 8. #16863569 | C2 | semidirect |
| 9. #16863513 | C2 | semidirect |
| 10. #16863511 | C2 | semidirect |
| 11. #578×C67 | C2 | semidirect |
| 18. #14524068 | C22 | semidirect |
| 23. C2×#11761615 | C22 | semidirect |
| 26. #14524050 | C22 | semidirect |
| 28. #14524032 | C22 | semidirect |
| 29. #14523979 | C22 | semidirect |
| 30. #14523978 | C22 | semidirect |
| 31. #14523970 | C22 | semidirect |
| 32. #14523970 | C22 | semidirect |
| 34. #14523962 | C22 | semidirect |
| 35. #14523959 | C22 | semidirect |
| 36. C8×Dic67 | C22 | semidirect |
| 37. 2−1+4×C67 | C22 | semidirect |
| 39. #137×C67 | C22 | semidirect |
| 43. C2×Q16×C67 | C22 | semidirect |
| 44. #131×C67 | C22 | semidirect |
| 150. C67 | #3290 | semidirect |
| 151. #578 | D67 | semidirect |
| 162. 2−1+4 | C2×D67 | semidirect |
| 167. #137 | C2×D67 | semidirect |
| 178. C2×Q16 | C2×D67 | semidirect |
| 185. #131 | C2×D67 | semidirect |