Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#13133214 | C2 | semidirect |
| 2. #16810999 | C2 | semidirect |
| 3. #16810971 | C2 | semidirect |
| 4. #16810818 | C2 | semidirect |
| 5. #16810756 | C2 | semidirect |
| 6. #16810676 | C2 | semidirect |
| 7. C53×#532 | C2 | semidirect |
| 11. C2×#11719922 | C22 | semidirect |
| 16. C4⋊#88322 | C22 | semidirect |
| 17. #13133137 | C22 | semidirect |
| 19. C4×#88322 | C22 | semidirect |
| 21. C4⋊Q8×C53 | C22 | semidirect |
| 22. #127×C53 | C22 | semidirect |
| 27. C4×D4×C53 | C22 | semidirect |
| 74. C2×C4×C53 | D8 | semidirect |
| 113. #532 | D53 | semidirect |
| 120. C53 | #3205 | semidirect |
| 126. C4⋊Q8 | C2×D53 | semidirect |
| 131. #127 | C2×D53 | semidirect |
| 136. C4×D4 | C2×D53 | semidirect |
| 193. C2×C4 | #11719922 | semidirect |