Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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×Q16×D67 | C2 | semidirect |
| 3. #16863838 | C2 | direct (N × H) |
| 4. C2×#14523989 | C2 | semidirect |
| 5. C2×#14523988 | C2 | semidirect |
| 6. C2×#14523986 | C2 | semidirect |
| 7. C2×#14523982 | C2 | semidirect |
| 8. C2×Q32×C67 | C2 | semidirect |
| 16. Q16×D67 | C22 | semidirect |
| 20. #14523989 | C22 | semidirect |
| 21. #14523988 | C22 | semidirect |
| 22. #14523986 | C22 | semidirect |
| 23. #14523982 | C22 | semidirect |
| 27. Q32×C67 | C22 | semidirect |
| 93. C2×C67 | #510 | semidirect |
| 98. C67 | C2×#510 | semidirect |
| 103. C2×Q32 | D67 | semidirect |
| 121. Q32 | C2×D67 | semidirect |
| 193. C2 | #16863838 | direct (N × H) |