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×C22⋊D67 |
| commutator | C4×C67 | C23×C4 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #518×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #518 | D67 |
| hypocenter | C67 | #2948 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #518 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863870 | C2 | semidirect |
| 3. #16863506 | C2 | semidirect |
| 4. C4×#11761613 | C2 | semidirect |
| 5. #16863432 | C2 | semidirect |
| 6. #16863401 | C2 | semidirect |
| 7. #16863400 | C2 | semidirect |
| 8. #16863352 | C2 | semidirect |
| 9. #518×C67 | C2 | semidirect |
| 11. C2×#11761613 | C4 | semidirect |
| 16. C4×D268 | C22 | semidirect |
| 20. #14523976 | C22 | semidirect |
| 21. #14523974 | C22 | semidirect |
| 22. #14523964 | C22 | semidirect |
| 23. #14523963 | C22 | semidirect |
| 24. #14523954 | C22 | semidirect |
| 25. C4×C67⋊C8 | C22 | semidirect |
| 28. C4×D4×C67 | C22 | semidirect |
| 35. C2×D268 | C2×C4 | semidirect |
| 38. #11761613 | C2×C4 | semidirect |
| 39. #11761613 | C2×C4 | semidirect |
| 41. C2×C67⋊C8 | C2×C4 | semidirect |
| 52. C2×D4×C67 | C2×C4 | semidirect |
| 109. C67 | #2948 | semidirect |
| 112. #518 | D67 | semidirect |
| 129. C4×D4 | C2×D67 | semidirect |
| 149. C2×D4 | C4×D67 | semidirect |