Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
458 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D4×D67 |
| commutator | C4×C67 | C23×C4 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #575×C67 | C2 |
| socle | C2×C67 | C2×C4×D4 |
| hypercenter | #575 | D67 |
| hypocenter | C67 | #2956 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #575 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864163 | C2 | semidirect |
| 2. #16863518 | C2 | semidirect |
| 3. #16863513 | C2 | semidirect |
| 4. #16863445 | C2 | semidirect |
| 5. C2×#14523970 | C2 | semidirect |
| 6. M16×Dic67 | C2 | semidirect |
| 9. #14524050 | C22 | semidirect |
| 14. #14523979 | C22 | semidirect |
| 15. #14523970 | C22 | semidirect |
| 16. #14523970 | C22 | semidirect |
| 17. #14523953 | C22 | semidirect |
| 18. C8×Dic67 | C22 | semidirect |
| 20. #137×C67 | C4 | semidirect |
| 21. AGL(1,ℤ/8)×C67 | C4 | semidirect |
| 44. Q16×C67 | C2×C4 | semidirect |
| 45. SD16×C67 | C2×C4 | semidirect |
| 46. D8×C67 | C2×C4 | semidirect |
| 86. C67 | #2956 | semidirect |
| 95. #137 | Dic67 | semidirect |
| 96. AGL(1,ℤ/8) | Dic67 | semidirect |
| 120. Q16 | C2×Dic67 | semidirect |
| 121. SD16 | C2×Dic67 | semidirect |
| 122. D8 | C2×Dic67 | semidirect |