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. #16864027 | C2 | semidirect |
| 3. #16863759 | C2 | semidirect |
| 4. #16863757 | C2 | semidirect |
| 5. #16863752 | C2 | semidirect |
| 6. #16863741 | C2 | semidirect |
| 7. #16863402 | C2 | semidirect |
| 8. #16863392 | C2 | semidirect |
| 9. C2×#14523963 | C2 | semidirect |
| 10. #16863354 | C2 | semidirect |
| 11. #417×C67 | C2 | semidirect |
| 15. #14524042 | C22 | semidirect |
| 18. #14524034 | C22 | semidirect |
| 26. #14523967 | C22 | semidirect |
| 27. #14523967 | C22 | semidirect |
| 30. #14523964 | C22 | semidirect |
| 31. #14523964 | C22 | semidirect |
| 34. #14523953 | C22 | semidirect |
| 35. C8×Dic67 | C22 | semidirect |
| 39. #103×C67 | C22 | semidirect |
| 40. #102×C67 | C22 | semidirect |
| 136. C67 | #3136 | semidirect |
| 144. #417 | D67 | semidirect |
| 167. #103 | C2×D67 | semidirect |
| 174. #102 | C2×D67 | semidirect |