Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 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 | #476×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #476 | D67 |
| hypocenter | C67 | #3295 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #476 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864107 | C2 | semidirect |
| 3. #16863744 | C2 | semidirect |
| 4. #16863716 | C2 | semidirect |
| 5. #16863626 | C2 | semidirect |
| 6. #16863597 | C2 | semidirect |
| 7. #16863548 | C2 | semidirect |
| 8. C4×#11761616 | C2 | semidirect |
| 9. #16863461 | C2 | semidirect |
| 10. #102×D67 | C2 | semidirect |
| 11. #476×C67 | C2 | semidirect |
| 14. C2×#11761617 | C22 | semidirect |
| 16. C2×C8×D67 | C22 | semidirect |
| 19. #14524023 | C22 | semidirect |
| 24. C4×Dic134 | C22 | semidirect |
| 27. C4⋊C4×D67 | C22 | semidirect |
| 28. #14523974 | C22 | semidirect |
| 29. #14523966 | C22 | semidirect |
| 30. #14523965 | C22 | semidirect |
| 32. #14523963 | C22 | semidirect |
| 33. #14523963 | C22 | semidirect |
| 34. (C2×D67)⋊C8 | C22 | semidirect |
| 35. C4×C67⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C67 | C22 | semidirect |
| 38. #106×C67 | C22 | semidirect |
| 39. C4⋊C8×C67 | C22 | semidirect |
| 101. D268 | SD16 | semidirect |
| 137. C67 | #3295 | semidirect |
| 142. #476 | D67 | semidirect |
| 154. C4⋊Q8 | C2×D67 | semidirect |
| 168. #106 | C2×D67 | semidirect |
| 169. C4⋊C8 | C2×D67 | semidirect |