Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524089 | C2 | semidirect |
| 2. C22×#11761613 | C2 | semidirect |
| 3. #16863963 | C2 | semidirect |
| 4. #16863540 | C2 | semidirect |
| 5. #16863528 | C2 | semidirect |
| 6. #16863402 | C2 | semidirect |
| 7. #16863392 | C2 | semidirect |
| 8. #16863364 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C67 | C2 | semidirect |
| 12. C2×#11761629 | C22 | semidirect |
| 18. C2×D4×D67 | C22 | semidirect |
| 20. C2×#11761613 | C22 | semidirect |
| 21. C22×C67⋊C8 | C22 | semidirect |
| 24. #14524014 | C22 | semidirect |
| 26. #14524002 | C22 | semidirect |
| 27. #14523967 | C22 | semidirect |
| 28. #14523965 | C22 | semidirect |
| 29. #14523964 | C22 | semidirect |
| 30. (C2×D67)⋊C8 | C22 | semidirect |
| 32. C22×D4×C67 | C22 | semidirect |
| 34. C2×SD16×C67 | C22 | semidirect |
| 35. C2×D8×C67 | C22 | semidirect |
| 36. C2×M16×C67 | C22 | semidirect |
| 50. C2×D268 | D4 | semidirect |
| 69. #41×C67 | D4 | semidirect |
| 152. C67 | #3008 | semidirect |
| 154. C2×AGL(1,ℤ/8) | D67 | semidirect |
| 172. C22×D4 | C2×D67 | semidirect |
| 174. C2×SD16 | C2×D67 | semidirect |
| 177. C2×D8 | C2×D67 | semidirect |
| 178. C2×M16 | C2×D67 | semidirect |
| 198. #41 | C22⋊D67 | semidirect |