Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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 | #433×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #433 | D67 |
| hypocenter | C67 | #3222 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #433 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864008 | C2 | semidirect |
| 3. #16863790 | C2 | semidirect |
| 4. #16863769 | C2 | semidirect |
| 5. #16863761 | C2 | semidirect |
| 6. #16863751 | C2 | semidirect |
| 7. #16863619 | C2 | semidirect |
| 8. #16863597 | C2 | semidirect |
| 9. #16863560 | C2 | semidirect |
| 10. #16863549 | C2 | semidirect |
| 11. #433×C67 | C2 | semidirect |
| 14. C2×Dic268 | C22 | semidirect |
| 17. C2×#11761617 | C22 | semidirect |
| 18. #14524043 | C22 | semidirect |
| 22. #14524035 | C22 | semidirect |
| 29. C4×Dic134 | C22 | semidirect |
| 30. #14523968 | C22 | semidirect |
| 33. #14523965 | C22 | semidirect |
| 35. C4⋊C8×C67 | C22 | semidirect |
| 37. #97×C67 | C22 | semidirect |
| 38. C4×C8×C67 | C22 | semidirect |
| 123. C67 | #3222 | semidirect |
| 134. #433 | D67 | semidirect |
| 154. C4⋊C8 | C2×D67 | semidirect |
| 160. #97 | C2×D67 | semidirect |
| 161. C4×C8 | C2×D67 | semidirect |