Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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 | #408×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #408 | D67 |
| hypocenter | C67 | #3200 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C2×#41 ◁ #408 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16863967 | C2 | semidirect |
| 3. #16863738 | C2 | semidirect |
| 4. #16863721 | C2 | semidirect |
| 5. #16863642 | C2 | semidirect |
| 6. #16863625 | C2 | semidirect |
| 7. #16863549 | C2 | semidirect |
| 8. #16863537 | C2 | semidirect |
| 9. #408×C67 | C2 | semidirect |
| 10. C22×Dic134 | C22 | semidirect |
| 21. #14524022 | C22 | semidirect |
| 27. #14524002 | C22 | semidirect |
| 28. #14523977 | C22 | semidirect |
| 29. #14523975 | C22 | semidirect |
| 30. #14523968 | C22 | semidirect |
| 31. #14523968 | C22 | semidirect |
| 35. C2×M16×C67 | C22 | semidirect |
| 36. C22×C8×C67 | C22 | semidirect |
| 38. C22⋊C8×C67 | C22 | semidirect |
| 138. C67 | #3200 | semidirect |
| 147. #408 | D67 | semidirect |
| 153. C2×M16 | C2×D67 | semidirect |
| 154. C22×C8 | C2×D67 | semidirect |
| 176. C22⋊C8 | C2×D67 | semidirect |