Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D67 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #462×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #462 | D67 |
| hypocenter | C67 | #3218 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #462 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4⋊Q8×D67 | C2 | semidirect |
| 3. #16863789 | C2 | semidirect |
| 4. #16863763 | C2 | semidirect |
| 5. #16863606 | C2 | semidirect |
| 6. #16863602 | C2 | semidirect |
| 7. #16863598 | C2 | semidirect |
| 8. #16863550 | C2 | semidirect |
| 10. #16863452 | C2 | semidirect |
| 11. #462×C67 | C2 | semidirect |
| 140. C67 | #3218 | semidirect |
| 146. #462 | D67 | semidirect |