Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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 | #3003 |
| 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. C23×D268 | C2 | semidirect |
| 2. C2×#14524071 | C2 | semidirect |
| 3. #16863907 | C2 | semidirect |
| 4. #16863549 | C2 | semidirect |
| 5. #16863532 | C2 | semidirect |
| 6. #16863402 | C2 | semidirect |
| 7. #407×C67 | C2 | semidirect |
| 9. C2×#11761628 | C22 | semidirect |
| 16. C2×#11761617 | C22 | semidirect |
| 17. C2×D536 | C22 | semidirect |
| 19. #14524022 | C22 | semidirect |
| 20. #14524017 | C22 | semidirect |
| 23. #14524002 | C22 | semidirect |
| 24. #14523965 | C22 | semidirect |
| 26. C2×M16×C67 | C22 | semidirect |
| 27. C22⋊C8×C67 | C22 | semidirect |
| 33. C2×Dic134 | C23 | semidirect |
| 40. C2×D268 | D4 | semidirect |
| 42. C2×D268 | C23 | semidirect |
| 48. C4⋊Dic67 | C23 | semidirect |
| 61. C2×C8×C67 | C23 | semidirect |
| 98. C22×C67 | AGL(1,ℤ/8) | semidirect |
| 118. C67 | #3003 | semidirect |
| 125. #407 | D67 | semidirect |
| 137. C2×M16 | C2×D67 | semidirect |
| 145. C22⋊C8 | C2×D67 | semidirect |
| 173. C2×C8 | C22×D67 | semidirect |
| 222. C22 | #14524071 | semidirect |