Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 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 | #2949 |
| 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. #16863873 | C2 | semidirect |
| 3. #16863496 | C2 | semidirect |
| 4. C4×#11761616 | C2 | semidirect |
| 5. #16863432 | C2 | semidirect |
| 6. #16863404 | C2 | semidirect |
| 8. #16863352 | C2 | semidirect |
| 11. C2×#11761616 | C4 | semidirect |
| 16. C4×Dic134 | C22 | semidirect |
| 20. #14523976 | C22 | semidirect |
| 21. #14523974 | C22 | semidirect |
| 22. #14523966 | C22 | semidirect |
| 24. #14523954 | C22 | semidirect |
| 25. C4×C67⋊C8 | C22 | semidirect |
| 34. C2×Dic134 | C2×C4 | semidirect |
| 37. #11761616 | C2×C4 | semidirect |
| 38. #11761616 | C2×C4 | semidirect |
| 40. C2×C67⋊C8 | C2×C4 | semidirect |
| 104. C67 | #2949 | semidirect |