Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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×#14524005 | C2 | semidirect |
| 3. #16863709 | C2 | semidirect |
| 4. #16863695 | C2 | semidirect |
| 5. #16863614 | C2 | semidirect |
| 6. #16863546 | C2 | semidirect |
| 8. #16863507 | C2 | semidirect |
| 9. #16863499 | C2 | semidirect |
| 10. #16863450 | C2 | semidirect |
| 11. #483×C67 | C2 | semidirect |
| 17. #14524034 | C22 | semidirect |
| 18. #14524032 | C22 | semidirect |
| 21. Q8×Dic67 | C22 | semidirect |
| 26. #14524005 | C22 | semidirect |
| 31. #14523976 | C22 | semidirect |
| 32. Dic67⋊C8 | C22 | semidirect |
| 35. #14523963 | C22 | semidirect |
| 37. #14523953 | C22 | semidirect |
| 40. #106×C67 | C22 | semidirect |
| 41. #103×C67 | C22 | semidirect |
| 141. C67 | #3114 | semidirect |
| 144. #483 | D67 | semidirect |
| 175. #106 | C2×D67 | semidirect |
| 177. #103 | C2×D67 | semidirect |