Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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 | #405×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #405 | D67 |
| hypocenter | C67 | #3136 |
| LCS | G ▷ C2×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 |
|---|---|---|
| 1. #16864024 | C2 | semidirect |
| 3. #16863761 | C2 | semidirect |
| 4. #16863756 | C2 | semidirect |
| 5. #16863751 | C2 | semidirect |
| 6. #16863743 | C2 | semidirect |
| 7. #16863402 | C2 | semidirect |
| 8. #16863398 | C2 | semidirect |
| 9. #16863393 | C2 | semidirect |
| 10. C2×#14523965 | C2 | semidirect |
| 11. #405×C67 | C2 | semidirect |
| 14. #14524043 | C22 | semidirect |
| 17. #14524035 | C22 | semidirect |
| 26. #14523968 | C22 | semidirect |
| 27. #14523968 | C22 | semidirect |
| 28. #14523968 | C22 | semidirect |
| 33. #14523965 | C22 | semidirect |
| 34. #14523965 | C22 | semidirect |
| 35. #14523965 | C22 | semidirect |
| 39. #97×C67 | C22 | semidirect |
| 40. C4×C8×C67 | C22 | semidirect |
| 136. C67 | #3136 | semidirect |
| 147. #405 | D67 | semidirect |
| 175. #97 | C2×D67 | semidirect |
| 176. C4×C8 | C2×D67 | semidirect |