Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 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 |
|---|---|---|
| 1. C2×#13133205 | C2 | semidirect |
| 2. #16811010 | C2 | semidirect |
| 3. #16810985 | C2 | semidirect |
| 4. #16810838 | C2 | semidirect |
| 5. #16810761 | C2 | semidirect |
| 6. #16810756 | C2 | semidirect |
| 7. #16810680 | C2 | semidirect |
| 8. C53×#532 | C2 | semidirect |
| 11. C2×#11719923 | C22 | semidirect |
| 19. C4⋊#88322 | C22 | semidirect |
| 20. #13133140 | C22 | semidirect |
| 23. #13133128 | C22 | semidirect |
| 25. C4⋊Q8×C53 | C22 | semidirect |
| 26. #127×C53 | C22 | semidirect |
| 31. C4×D4×C53 | C22 | semidirect |
| 121. #532 | D53 | semidirect |
| 129. C53 | #3213 | semidirect |
| 135. C4⋊Q8 | C2×D53 | semidirect |
| 136. #127 | C2×D53 | semidirect |
| 145. C4×D4 | C2×D53 | semidirect |