Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. #16863733 | C2 | semidirect |
| 3. #16863730 | C2 | semidirect |
| 4. #16863637 | C2 | semidirect |
| 5. #16863635 | C2 | semidirect |
| 6. #16863553 | C2 | semidirect |
| 7. #16863550 | C2 | semidirect |
| 9. #467×C67 | C2 | semidirect |
| 12. C2×Dic268 | C22 | semidirect |
| 13. C2×#11761618 | C22 | semidirect |
| 23. #14523977 | C22 | semidirect |
| 24. #14523976 | C22 | semidirect |
| 25. #14523968 | C22 | semidirect |
| 26. #14523967 | C22 | semidirect |
| 27. #14523966 | C22 | semidirect |
| 30. C2×Q16×C67 | C22 | semidirect |
| 33. #107×C67 | C22 | semidirect |
| 34. #103×C67 | C22 | semidirect |
| 71. C22×D67 | Q16 | semidirect |
| 118. C67 | #3189 | semidirect |
| 124. #467 | D67 | semidirect |
| 132. C2×Q16 | C2×D67 | semidirect |
| 146. #107 | C2×D67 | semidirect |
| 150. #103 | C2×D67 | semidirect |