Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
466 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 466 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. #16863909 | C2 | semidirect |
| 2. C2×#14524014 | C2 | semidirect |
| 3. #16863724 | C2 | semidirect |
| 4. #16863718 | C2 | semidirect |
| 5. #16863710 | C2 | semidirect |
| 6. #16863648 | C2 | semidirect |
| 7. #16863639 | C2 | semidirect |
| 8. #16863540 | C2 | semidirect |
| 9. #16863530 | C2 | semidirect |
| 10. #16863358 | C2 | semidirect |
| 11. #450×C67 | C2 | semidirect |
| 12. C2×#11761629 | C22 | semidirect |
| 15. C2×#11761613 | C22 | semidirect |
| 16. C2×#11761611 | C22 | semidirect |
| 18. #14524019 | C22 | semidirect |
| 19. #14524018 | C22 | semidirect |
| 28. #14524001 | C22 | semidirect |
| 31. #14523977 | C22 | semidirect |
| 32. #14523974 | C22 | semidirect |
| 33. #14523967 | C22 | semidirect |
| 34. #14523965 | C22 | semidirect |
| 35. #14523964 | C22 | semidirect |
| 37. (C2×D67)⋊C8 | C22 | semidirect |
| 39. C2×SD16×C67 | C22 | semidirect |
| 41. #102×C67 | C22 | semidirect |
| 159. C67 | #3194 | semidirect |
| 167. #450 | D67 | semidirect |
| 175. C2×SD16 | C2×D67 | semidirect |
| 198. #102 | C2×D67 | semidirect |