Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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 | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #431×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #431 | D67 |
| hypocenter | C67 | #3208 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #431 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16863953 | C2 | semidirect |
| 3. #16863769 | C2 | semidirect |
| 4. #16863743 | C2 | semidirect |
| 5. #16863597 | C2 | semidirect |
| 6. #16863549 | C2 | semidirect |
| 7. #431×C67 | C2 | semidirect |
| 11. C2×#11761617 | C22 | semidirect |
| 12. #14524043 | C22 | semidirect |
| 13. #14524043 | C22 | semidirect |
| 22. C4×Dic134 | C22 | semidirect |
| 24. #14523965 | C22 | semidirect |
| 26. C4⋊C8×C67 | C22 | semidirect |
| 28. C4×C8×C67 | C22 | semidirect |
| 65. C2×C4×C67 | SD16 | semidirect |
| 105. C67 | #3208 | semidirect |
| 112. #431 | D67 | semidirect |
| 130. C4⋊C8 | C2×D67 | semidirect |
| 133. C4×C8 | C2×D67 | semidirect |
| 180. C2×C4 | #11761617 | semidirect |