Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
584 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#14524071 | C2 | semidirect |
| 2. C2×#14524069 | C2 | semidirect |
| 3. C2×#14524039 | C2 | semidirect |
| 4. #16863864 | C2 | semidirect |
| 5. #16863595 | C2 | semidirect |
| 6. #16863590 | C2 | semidirect |
| 7. #16863419 | C2 | semidirect |
| 8. #16863400 | C2 | semidirect |
| 9. #418×C67 | C2 | semidirect |
| 15. C2×#11761617 | C22 | semidirect |
| 16. C2×#11761616 | C22 | semidirect |
| 17. C2×D536 | C22 | semidirect |
| 18. C2×#11761613 | C22 | semidirect |
| 23. #14524008 | C22 | semidirect |
| 24. #14524005 | C22 | semidirect |
| 29. Dic67⋊C8 | C22 | semidirect |
| 30. #14523963 | C22 | semidirect |
| 34. #102×C67 | C22 | semidirect |
| 37. #11761628 | D4 | semidirect |
| 101. D268 | C2×D4 | semidirect |
| 105. Dic134 | C2×D4 | semidirect |
| 125. Dic67 | AGL(1,ℤ/8) | semidirect |
| 133. C67 | #3038 | semidirect |
| 142. #418 | D67 | semidirect |
| 167. #102 | C2×D67 | semidirect |