Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14524063 | C2 | semidirect |
| 3. #16863960 | C2 | semidirect |
| 4. #16863877 | C2 | semidirect |
| 5. #16863621 | C2 | semidirect |
| 6. #16863614 | C2 | semidirect |
| 7. #16863595 | C2 | semidirect |
| 8. #16863590 | C2 | semidirect |
| 9. #16863424 | C2 | semidirect |
| 10. C2×#14523963 | C2 | semidirect |
| 11. #417×C67 | C2 | semidirect |
| 16. C2×#11761618 | C22 | semidirect |
| 18. C2×#11761616 | C22 | semidirect |
| 19. C2×#11761615 | C22 | semidirect |
| 21. C2×#11761613 | C22 | semidirect |
| 28. #14524008 | C22 | semidirect |
| 29. #14524005 | C22 | semidirect |
| 34. Dic67⋊C8 | C22 | semidirect |
| 35. Dic67⋊C8 | C22 | semidirect |
| 41. #103×C67 | C22 | semidirect |
| 42. #102×C67 | C22 | semidirect |
| 45. #11761628 | D4 | semidirect |
| 155. C67 | #3045 | semidirect |
| 165. #417 | D67 | semidirect |
| 194. #103 | C2×D67 | semidirect |
| 197. #102 | C2×D67 | semidirect |