Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
472 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 189 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×#13133223 | C2 | semidirect |
| 3. #16810741 | C2 | direct (N × H) |
| 4. C2×#13133153 | C2 | semidirect |
| 5. C2×#13133145 | C2 | semidirect |
| 6. C2×C4×C8×C53 | C2 | semidirect |
| 8. #13133239 | C4 | semidirect |
| 10. C2×Dic212 | C4 | semidirect |
| 11. C2×#11719913 | C4 | semidirect |
| 12. C2×D424 | C4 | semidirect |
| 14. #13133223 | C22 | semidirect |
| 18. #13133153 | C22 | semidirect |
| 19. #13133145 | C22 | semidirect |
| 23. C4×C8×C53 | C22 | semidirect |
| 47. Dic212 | C2×C4 | semidirect |
| 48. D424 | C2×C4 | semidirect |
| 49. #11719913 | C2×C4 | semidirect |
| 91. C2×C53 | #443 | semidirect |
| 99. C2×C4×C8 | D53 | semidirect |
| 100. C53 | C2×#443 | semidirect |
| 117. C4×C8 | C2×D53 | semidirect |
| 185. C2 | #16810741 | direct (N × H) |