Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
656 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 173 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×#13133245 | C2 | semidirect |
| 2. #16811173 | C2 | semidirect |
| 3. C2×#13133214 | C2 | semidirect |
| 4. #16811012 | C2 | semidirect |
| 5. #16811000 | C2 | semidirect |
| 6. #16810996 | C2 | semidirect |
| 7. C4×M16×C53 | C2 | semidirect |
| 12. C2×#11719913 | C22 | semidirect |
| 13. C2×D424 | C22 | semidirect |
| 14. #13133217 | C22 | semidirect |
| 18. #13133214 | C22 | semidirect |
| 19. #13133205 | C22 | semidirect |
| 24. #97×C53 | C22 | semidirect |
| 25. C4×C8×C53 | C22 | semidirect |
| 41. M16×C53 | D4 | semidirect |
| 71. C8×C53 | C2×D4 | semidirect |
| 82. C4×C53 | AGL(1,ℤ/8) | semidirect |
| 97. C4×M16 | D53 | semidirect |
| 98. C53 | #3151 | semidirect |
| 115. #97 | C2×D53 | semidirect |
| 116. C4×C8 | C2×D53 | semidirect |
| 134. M16 | D212 | semidirect |
| 162. C8 | C2×D212 | semidirect |
| 174. C4 | #13133245 | semidirect |