Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#11761615 | C2 | semidirect |
| 3. C2×#14524019 | C2 | semidirect |
| 4. #16863557 | C2 | direct (N × H) |
| 5. C2×#14523967 | C2 | semidirect |
| 6. C2×#14523965 | C2 | semidirect |
| 7. C2×(C2×D67)⋊C8 | C2 | semidirect |
| 8. C22×Q16×C67 | C2 | semidirect |
| 18. C2×#11761615 | C22 | semidirect |
| 21. #14524019 | C22 | semidirect |
| 25. #14523967 | C22 | semidirect |
| 26. #14523965 | C22 | semidirect |
| 27. (C2×D67)⋊C8 | C22 | semidirect |
| 31. C2×Q16×C67 | C22 | semidirect |
| 129. C2×C67 | #452 | semidirect |
| 136. C67 | C2×#452 | semidirect |
| 138. C22×Q16 | D67 | semidirect |
| 156. C2×Q16 | C2×D67 | semidirect |
| 267. C2 | #16863557 | direct (N × H) |