Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14524032 | C2 | semidirect |
| 3. C2×D4×Dic67 | C2 | semidirect |
| 4. #16863613 | C2 | direct (N × H) |
| 5. C2×Dic67⋊C8 | C2 | semidirect |
| 6. C2×#14523967 | C2 | semidirect |
| 7. C2×#14523965 | C2 | semidirect |
| 8. C22×SD16×C67 | C2 | semidirect |
| 15. #14524032 | C22 | semidirect |
| 17. D4×Dic67 | C22 | semidirect |
| 23. Dic67⋊C8 | C22 | semidirect |
| 24. #14523967 | C22 | semidirect |
| 25. #14523965 | C22 | semidirect |
| 29. C2×SD16×C67 | C22 | semidirect |
| 118. C2×C67 | #463 | semidirect |
| 124. C67 | C2×#463 | semidirect |
| 125. C22×SD16 | D67 | semidirect |
| 138. C2×SD16 | C2×D67 | semidirect |
| 243. C2 | #16863613 | direct (N × H) |