Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×D268 |
| commutator | C4×C67 | C25 |
| Frattini | C4 | C24×D67 |
| Fitting | #568×C67 | C2 |
| socle | C2×C67 | C23×D4 |
| hypercenter | #568 | D67 |
| hypocenter | C67 | #3586 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #568 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864232 | C2 | semidirect |
| 2. C2×#14524090 | C2 | semidirect |
| 3. #16864213 | C2 | semidirect |
| 4. #16864208 | C2 | semidirect |
| 5. #16864196 | C2 | semidirect |
| 6. C2×#14524076 | C2 | semidirect |
| 7. #568×C67 | C2 | semidirect |
| 10. #14524090 | C22 | semidirect |
| 11. #14524090 | C22 | semidirect |
| 12. #14524089 | C22 | semidirect |
| 15. C2×#11761628 | C22 | semidirect |
| 18. C22×Dic134 | C22 | semidirect |
| 20. #14524076 | C22 | semidirect |
| 21. #14524076 | C22 | semidirect |
| 22. #14524076 | C22 | semidirect |
| 23. #14524071 | C22 | semidirect |
| 24. #14524071 | C22 | semidirect |
| 25. #14524065 | C22 | semidirect |
| 26. C2×Dic268 | C22 | semidirect |
| 27. C2×#11761617 | C22 | semidirect |
| 29. #131×C67 | C22 | semidirect |
| 30. C2×M16×C67 | C22 | semidirect |
| 113. C67 | #3586 | semidirect |
| 120. #568 | D67 | semidirect |
| 142. #131 | C2×D67 | semidirect |
| 143. C2×M16 | C2×D67 | semidirect |