Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
232 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 67 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. M32×D67 | C2 | semidirect |
| 3. #106×D67 | C2 | semidirect |
| 4. #16863207 | C2 | semidirect |
| 5. #16863206 | C2 | semidirect |
| 6. #16863205 | C2 | semidirect |
| 7. #360×C67 | C2 | semidirect |
| 9. #14524066 | C4 | semidirect |
| 13. #14524062 | C4 | semidirect |
| 14. Q16×D67 | C4 | semidirect |
| 16. D8×D67 | C4 | semidirect |
| 19. #14523983 | C22 | semidirect |
| 22. #14523975 | C22 | semidirect |
| 25. M32×C67 | C22 | semidirect |
| 26. #106×C67 | C22 | semidirect |
| 38. Dic268 | C2×C4 | semidirect |
| 43. D536 | C2×C4 | semidirect |
| 54. Q16×C67 | C2×C4 | semidirect |
| 56. D8×C67 | C2×C4 | semidirect |
| 110. D67 | #360 | direct (N × H) |
| 112. C67 | C2×#360 | semidirect |
| 119. #360 | D67 | direct (N × H) |
| 134. M32 | C2×D67 | semidirect |
| 138. #106 | C2×D67 | semidirect |
| 153. Q16 | C4×D67 | semidirect |
| 160. D8 | C4×D67 | semidirect |