Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
488 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D67 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #476×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #476 | D67 |
| hypocenter | C67 | #3109 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #476 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16863947 | C2 | semidirect |
| 2. C4×D4×D67 | C2 | semidirect |
| 3. #16863716 | C2 | semidirect |
| 4. #16863683 | C2 | semidirect |
| 5. #16863592 | C2 | semidirect |
| 6. #16863591 | C2 | semidirect |
| 7. #16863531 | C2 | semidirect |
| 8. #16863507 | C2 | semidirect |
| 9. #16863505 | C2 | semidirect |
| 10. #16863452 | C2 | semidirect |
| 11. #476×C67 | C2 | semidirect |
| 17. #14524040 | C22 | semidirect |
| 25. #14524005 | C22 | semidirect |
| 31. #14523974 | C22 | semidirect |
| 32. C4⋊(C67⋊C8) | C22 | semidirect |
| 33. #14523965 | C22 | semidirect |
| 35. #14523963 | C22 | semidirect |
| 37. #14523953 | C22 | semidirect |
| 38. C4⋊Q8×C67 | C22 | semidirect |
| 40. #106×C67 | C22 | semidirect |
| 41. C4⋊C8×C67 | C22 | semidirect |
| 93. D4×C67 | #41 | semidirect |
| 112. D268 | #41 | semidirect |
| 155. C67 | #3109 | semidirect |
| 160. #476 | D67 | semidirect |
| 172. C4⋊Q8 | C2×D67 | semidirect |
| 189. #106 | C2×D67 | semidirect |
| 191. C4⋊C8 | C2×D67 | semidirect |
| 256. D4 | #11761629 | semidirect |