Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
412 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 412 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 | C2×D4×D67 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #488×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #488 | D67 |
| hypocenter | C67 | C2×#488 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #488 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #125×D67 | C2 | semidirect |
| 3. #16863753 | C2 | semidirect |
| 4. #16863752 | C2 | semidirect |
| 5. #16863751 | C2 | semidirect |
| 6. #16863750 | C2 | semidirect |
| 7. #16863749 | C2 | semidirect |
| 8. #103×D67 | C2 | semidirect |
| 10. C4×C8×D67 | C2 | semidirect |
| 11. #488×C67 | C2 | semidirect |
| 15. #14524035 | C22 | semidirect |
| 16. #14524034 | C22 | semidirect |
| 26. #14523968 | C22 | semidirect |
| 27. #14523967 | C22 | semidirect |
| 28. #14523966 | C22 | semidirect |
| 32. C4×C67⋊C8 | C22 | semidirect |
| 33. C8×Dic67 | C22 | semidirect |
| 34. #125×C67 | C22 | semidirect |
| 36. #103×C67 | C22 | semidirect |
| 38. C4×C8×C67 | C22 | semidirect |
| 114. D67 | #488 | direct (N × H) |
| 116. C67 | C2×#488 | semidirect |
| 124. #488 | D67 | direct (N × H) |
| 134. #125 | C2×D67 | semidirect |
| 147. #103 | C2×D67 | semidirect |
| 154. C4×C8 | C2×D67 | semidirect |