Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. #16863930 | C2 | semidirect |
| 2. #16863778 | C2 | semidirect |
| 3. #16863750 | C2 | semidirect |
| 4. #16863615 | C2 | semidirect |
| 5. #16863608 | C2 | semidirect |
| 6. #16863552 | C2 | semidirect |
| 7. #16863547 | C2 | semidirect |
| 8. #16863535 | C2 | semidirect |
| 10. #16863449 | C2 | semidirect |
| 11. C2×#124×C67 | C2 | semidirect |
| 12. C2×#11761618 | C22 | semidirect |
| 14. C2×#11761615 | C22 | semidirect |
| 17. #14524035 | C22 | semidirect |
| 18. #14524031 | C22 | semidirect |
| 22. C4×Dic134 | C22 | semidirect |
| 23. C4×D268 | C22 | semidirect |
| 26. C4⋊(C67⋊C8) | C22 | semidirect |
| 27. #14523967 | C22 | semidirect |
| 28. #14523967 | C22 | semidirect |
| 33. C4×C67⋊C8 | C22 | semidirect |
| 144. C67 | #3211 | semidirect |
| 146. C2×#124 | D67 | semidirect |