Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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 | #3006 |
| 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. C22×#11761628 | C2 | semidirect |
| 2. C2×#14524071 | C2 | semidirect |
| 3. C2×#14524017 | C2 | semidirect |
| 4. #16863543 | C2 | semidirect |
| 5. #16863537 | C2 | semidirect |
| 6. #16863532 | C2 | semidirect |
| 7. #16863398 | C2 | semidirect |
| 8. #407×C67 | C2 | semidirect |
| 13. C2×#11761628 | C22 | semidirect |
| 14. C22×Dic134 | C22 | semidirect |
| 15. C22×D268 | C22 | semidirect |
| 16. C22×D268 | C22 | semidirect |
| 21. C2×#11761617 | C22 | semidirect |
| 22. C2×D536 | C22 | semidirect |
| 26. #14524017 | C22 | semidirect |
| 27. C2×C4⋊Dic67 | C22 | semidirect |
| 29. #14523968 | C22 | semidirect |
| 30. #14523965 | C22 | semidirect |
| 32. C2×M16×C67 | C22 | semidirect |
| 33. C22⋊C8×C67 | C22 | semidirect |
| 34. C22⋊C8×C67 | C22 | semidirect |
| 42. #11761628 | D4 | semidirect |
| 115. D268 | C2×D4 | semidirect |
| 120. Dic134 | C2×D4 | semidirect |
| 131. C22×C67 | AGL(1,ℤ/8) | semidirect |
| 156. C67 | #3006 | semidirect |
| 164. #407 | D67 | semidirect |
| 180. C2×M16 | C2×D67 | semidirect |
| 189. C22⋊C8 | C2×D67 | semidirect |
| 190. C22⋊C8 | C2×D67 | semidirect |
| 295. C22 | #14524071 | semidirect |