Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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 |
|---|---|---|
| 2. #16810997 | C2 | semidirect |
| 3. #16810971 | C2 | semidirect |
| 4. #16810823 | C2 | semidirect |
| 5. #16810773 | C2 | semidirect |
| 6. #16810676 | C2 | semidirect |
| 7. C53×#533 | C2 | semidirect |
| 11. C2×#11719924 | C22 | semidirect |
| 16. C4⋊#88322 | C22 | semidirect |
| 17. #13133137 | C22 | semidirect |
| 19. C4×#88322 | C22 | semidirect |
| 20. C4⋊Q8×C53 | C22 | semidirect |
| 21. C4⋊Q8×C53 | C22 | semidirect |
| 26. C4×Q8×C53 | C22 | semidirect |
| 69. C2×C4×C53 | SD16 | semidirect |
| 105. #533 | D53 | semidirect |
| 112. C53 | #3208 | semidirect |
| 117. C4⋊Q8 | C2×D53 | semidirect |
| 118. C4⋊Q8 | C2×D53 | semidirect |
| 127. C4×Q8 | C2×D53 | semidirect |
| 180. C2×C4 | #11719924 | semidirect |