Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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 | #424×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #424 | D67 |
| hypocenter | C67 | #3081 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #424 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864024 | C2 | semidirect |
| 3. #16863697 | C2 | semidirect |
| 4. #16863697 | C2 | semidirect |
| 5. #16863687 | C2 | semidirect |
| 6. #16863677 | C2 | semidirect |
| 7. #16863438 | C2 | semidirect |
| 8. #16863434 | C2 | semidirect |
| 11. #424×C67 | C2 | semidirect |
| 13. #14524043 | C22 | semidirect |
| 15. #14524035 | 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. C4⋊C8×C67 | C22 | semidirect |
| 40. C4⋊C8×C67 | C22 | semidirect |
| 45. C2×D268 | Q8 | semidirect |
| 125. C67 | #3081 | semidirect |
| 134. #424 | D67 | semidirect |
| 160. C4⋊C8 | C2×D67 | semidirect |
| 161. C4⋊C8 | C2×D67 | semidirect |