Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14524074 | C2 | semidirect |
| 2. C2×#14524069 | C2 | semidirect |
| 3. C2×#14524065 | C2 | semidirect |
| 4. #16863970 | C2 | semidirect |
| 5. #16863963 | C2 | semidirect |
| 6. #16863787 | C2 | semidirect |
| 7. #16863782 | C2 | semidirect |
| 8. #16863777 | C2 | semidirect |
| 9. #16863767 | C2 | semidirect |
| 10. #16863351 | C2 | semidirect |
| 11. C22×SD16×C67 | C2 | semidirect |
| 17. C2×Dic268 | C22 | semidirect |
| 18. C2×#11761618 | C22 | semidirect |
| 19. C2×#11761617 | C22 | semidirect |
| 20. C2×#11761617 | C22 | semidirect |
| 22. C2×#11761615 | C22 | semidirect |
| 23. C2×D536 | C22 | semidirect |
| 26. #14524041 | C22 | semidirect |
| 28. #14524032 | C22 | semidirect |
| 35. #14523953 | C22 | semidirect |
| 36. C8×Dic67 | C22 | semidirect |
| 64. #11761612 | D4 | semidirect |
| 85. C2×C8×C67 | D4 | semidirect |
| 149. C67 | #3154 | semidirect |
| 153. C22×SD16 | D67 | semidirect |
| 228. C2×C8 | C22⋊D67 | semidirect |