Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C4×C67 | C23×C4 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #405×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #405 | D67 |
| hypocenter | C67 | #2948 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863870 | C2 | semidirect |
| 3. #16863509 | C2 | semidirect |
| 4. C4×D536 | C2 | semidirect |
| 5. #16863434 | C2 | semidirect |
| 6. #16863402 | C2 | semidirect |
| 7. #405×C67 | C2 | semidirect |
| 9. C2×D536 | C4 | semidirect |
| 12. C4×D268 | C22 | semidirect |
| 16. #14523977 | C22 | semidirect |
| 17. #14523975 | C22 | semidirect |
| 18. #14523965 | C22 | semidirect |
| 22. #97×C67 | C22 | semidirect |
| 23. C4×C8×C67 | C22 | semidirect |
| 27. C2×D268 | C2×C4 | semidirect |
| 30. D536 | C2×C4 | semidirect |
| 31. D536 | C2×C4 | semidirect |
| 38. C2×C8×C67 | C2×C4 | semidirect |
| 78. C67 | #2948 | semidirect |
| 85. #405 | D67 | semidirect |
| 100. #97 | C2×D67 | semidirect |
| 101. C4×C8 | C2×D67 | semidirect |
| 112. C2×C8 | C4×D67 | semidirect |