Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
616 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 221 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. C2×C4×D212 | C2 | semidirect |
| 3. C4×#11719922 | C2 | direct (N × H) |
| 4. C2×#13133150 | C2 | semidirect |
| 5. C2×#13133138 | C2 | semidirect |
| 6. C2×#13133137 | C2 | semidirect |
| 7. C2×C4×#88322 | C2 | semidirect |
| 8. C2×C4×D4×C53 | C2 | semidirect |
| 11. C2×#11719922 | C4 | direct (N × H) |
| 16. C4×D212 | C22 | semidirect |
| 19. #13133150 | C22 | semidirect |
| 20. #13133138 | C22 | semidirect |
| 21. #13133137 | C22 | semidirect |
| 22. C4×#88322 | C22 | semidirect |
| 26. C4×D4×C53 | C22 | semidirect |
| 34. C2×D4×C53 | C2×C4 | semidirect |
| 45. C2×D212 | C2×C4 | semidirect |
| 54. #11719922 | C2×C4 | direct (N × H) |
| 59. C2×#88322 | C2×C4 | semidirect |
| 73. D4×C53 | C22×C4 | semidirect |
| 78. C2×C4×C53 | D8 | semidirect |
| 89. D212 | C22×C4 | semidirect |
| 92. #88322 | C22×C4 | semidirect |
| 108. C4×C53 | C2×D8 | semidirect |
| 114. C2×C53 | C4×D8 | semidirect |
| 121. C2×C4×D4 | D53 | semidirect |
| 127. C53 | C2×C4×D8 | semidirect |
| 139. C4×D4 | C2×D53 | semidirect |
| 157. C2×D4 | C4×D53 | semidirect |
| 195. D4 | C2×C4×D53 | semidirect |
| 203. C2×C4 | #11719922 | direct (N × H) |
| 228. C4 | C2×#11719922 | direct (N × H) |
| 233. C2 | C4×#11719922 | direct (N × H) |