Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
760 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13133248 | C2 | semidirect |
| 3. #16810800 | C2 | direct (N × H) |
| 4. C2×#13133145 | C2 | semidirect |
| 5. C2×#13133134 | C2 | semidirect |
| 6. C2×#124×C53 | C2 | semidirect |
| 15. #13133248 | C22 | semidirect |
| 18. C2×#11719917 | C22 | semidirect |
| 19. #13133145 | C22 | semidirect |
| 20. #13133134 | C22 | semidirect |
| 21. C22×Q8×C53 | C22 | semidirect |
| 24. #124×C53 | C22 | semidirect |
| 26. C2×C42×C53 | C22 | semidirect |
| 32. C2×Q8×C53 | C23 | semidirect |
| 58. C42×C53 | C23 | semidirect |
| 62. #11719917 | C23 | semidirect |
| 117. C2×C53 | #455 | semidirect |
| 122. C2×#124 | D53 | semidirect |
| 126. C53 | C2×#455 | semidirect |
| 132. C22×Q8 | C2×D53 | semidirect |
| 142. #124 | C2×D53 | semidirect |
| 144. C2×C42 | C2×D53 | semidirect |
| 159. C2×Q8 | C22×D53 | semidirect |
| 183. C42 | C22×D53 | semidirect |
| 237. C2 | #16810800 | direct (N × H) |