Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16864024 | C2 | semidirect |
| 3. #16863759 | C2 | semidirect |
| 4. #16863757 | C2 | semidirect |
| 5. #16863752 | C2 | semidirect |
| 6. #16863741 | C2 | semidirect |
| 7. #16863400 | C2 | semidirect |
| 8. #16863397 | C2 | semidirect |
| 9. C2×#14523965 | C2 | semidirect |
| 10. #16863351 | C2 | semidirect |
| 11. #416×C67 | C2 | semidirect |
| 15. #14524042 | C22 | semidirect |
| 18. #14524034 | C22 | semidirect |
| 26. #14523967 | C22 | semidirect |
| 29. #14523964 | C22 | semidirect |
| 32. #14523953 | C22 | semidirect |
| 33. C8×Dic67 | C22 | semidirect |
| 37. #103×C67 | C22 | semidirect |
| 38. #103×C67 | C22 | semidirect |
| 39. #102×C67 | C22 | semidirect |
| 40. #102×C67 | C22 | semidirect |
| 136. C67 | #3136 | semidirect |
| 145. #416 | D67 | semidirect |
| 166. #103 | C2×D67 | semidirect |
| 167. #103 | C2×D67 | semidirect |
| 173. #102 | C2×D67 | semidirect |
| 174. #102 | C2×D67 | semidirect |