Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D268 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #424×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #424 | D67 |
| hypocenter | C67 | #3045 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #424 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524071 | C2 | semidirect |
| 2. C2×#14524065 | C2 | semidirect |
| 3. #16863965 | C2 | semidirect |
| 4. #16863876 | C2 | semidirect |
| 5. #16863619 | C2 | semidirect |
| 6. #16863612 | C2 | semidirect |
| 7. #16863597 | C2 | semidirect |
| 8. #16863592 | C2 | semidirect |
| 9. #16863398 | C2 | semidirect |
| 10. C2×#14523965 | C2 | semidirect |
| 11. #424×C67 | C2 | semidirect |
| 17. C2×Dic268 | C22 | semidirect |
| 19. C2×#11761617 | C22 | semidirect |
| 20. C2×#11761617 | C22 | semidirect |
| 22. C2×D536 | C22 | semidirect |
| 28. C4×Dic134 | C22 | semidirect |
| 29. C4×D268 | C22 | semidirect |
| 34. #14523968 | C22 | semidirect |
| 37. #14523965 | C22 | semidirect |
| 41. C4⋊C8×C67 | C22 | semidirect |
| 42. C4⋊C8×C67 | C22 | semidirect |
| 47. #11761628 | D4 | semidirect |
| 155. C67 | #3045 | semidirect |
| 164. #424 | D67 | semidirect |
| 192. C4⋊C8 | C2×D67 | semidirect |
| 193. C4⋊C8 | C2×D67 | semidirect |