Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 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 | #408×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #408 | D67 |
| hypocenter | C67 | #3096 |
| 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 |
|---|---|---|
| 2. #16863879 | C2 | semidirect |
| 3. #16863721 | C2 | semidirect |
| 4. #16863721 | C2 | semidirect |
| 5. #16863715 | C2 | semidirect |
| 6. #16863710 | C2 | semidirect |
| 7. #16863438 | C2 | semidirect |
| 8. #16863434 | C2 | semidirect |
| 9. #16863402 | C2 | semidirect |
| 10. C2×#14523965 | C2 | semidirect |
| 11. #408×C67 | C2 | semidirect |
| 23. #14524002 | C22 | semidirect |
| 25. C2×C4⋊Dic67 | C22 | semidirect |
| 26. #14523977 | C22 | semidirect |
| 27. #14523977 | C22 | semidirect |
| 28. #14523977 | C22 | semidirect |
| 29. #14523975 | C22 | semidirect |
| 30. #14523975 | C22 | semidirect |
| 31. #14523975 | C22 | semidirect |
| 39. C22⋊C8×C67 | C22 | semidirect |
| 40. C22⋊C8×C67 | C22 | semidirect |
| 135. C67 | #3096 | semidirect |
| 146. #408 | D67 | semidirect |
| 174. C22⋊C8 | C2×D67 | semidirect |
| 175. C22⋊C8 | C2×D67 | semidirect |