Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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 | #407×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #407 | D67 |
| hypocenter | C67 | #3193 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #407 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524022 | C2 | semidirect |
| 3. #16863732 | C2 | semidirect |
| 4. #16863710 | C2 | semidirect |
| 5. #16863642 | C2 | semidirect |
| 6. #16863549 | C2 | semidirect |
| 7. #16863537 | C2 | semidirect |
| 8. #407×C67 | C2 | semidirect |
| 9. C22×Dic134 | C22 | semidirect |
| 12. C2×#11761617 | C22 | semidirect |
| 16. #14524022 | C22 | semidirect |
| 22. C2×C4⋊Dic67 | C22 | semidirect |
| 26. #14523977 | C22 | semidirect |
| 27. #14523968 | C22 | semidirect |
| 28. #14523965 | C22 | semidirect |
| 30. C2×M16×C67 | C22 | semidirect |
| 32. C22⋊C8×C67 | C22 | semidirect |
| 130. C67 | #3193 | semidirect |
| 138. #407 | D67 | semidirect |
| 144. C2×M16 | C2×D67 | semidirect |
| 162. C22⋊C8 | C2×D67 | semidirect |