Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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. #16863932 | C2 | semidirect |
| 2. C2×#14524032 | C2 | semidirect |
| 3. #16863781 | C2 | semidirect |
| 4. #16863752 | C2 | semidirect |
| 5. #16863620 | C2 | semidirect |
| 6. #16863614 | C2 | semidirect |
| 7. #16863546 | C2 | semidirect |
| 8. #16863535 | C2 | semidirect |
| 10. #16863446 | C2 | semidirect |
| 11. #451×C67 | C2 | semidirect |
| 14. C2×#11761615 | C22 | semidirect |
| 17. #14524034 | C22 | semidirect |
| 22. #14524032 | C22 | semidirect |
| 25. Q8×Dic67 | C22 | semidirect |
| 26. #14524005 | C22 | semidirect |
| 32. Dic67⋊C8 | C22 | semidirect |
| 33. #14523967 | C22 | semidirect |
| 37. C8×Dic67 | C22 | semidirect |
| 39. C2×Q16×C67 | C22 | semidirect |
| 41. #103×C67 | C22 | semidirect |
| 144. C67 | #3211 | semidirect |
| 151. #451 | D67 | semidirect |
| 158. C2×Q16 | C2×D67 | semidirect |
| 181. #103 | C2×D67 | semidirect |