Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13133243 | C2 | semidirect |
| 2. #16811173 | C2 | semidirect |
| 3. #16811010 | C2 | semidirect |
| 4. #16810999 | C2 | semidirect |
| 5. #16810995 | C2 | semidirect |
| 6. C4×#11719917 | C2 | semidirect |
| 7. C2×#127×C53 | C2 | semidirect |
| 10. C2×#11719923 | C22 | semidirect |
| 11. C2×#11719922 | C22 | semidirect |
| 13. #13133217 | C22 | semidirect |
| 14. #13133214 | C22 | semidirect |
| 15. #13133205 | C22 | semidirect |
| 18. #13133128 | C22 | semidirect |
| 19. C4×#88322 | C22 | semidirect |
| 48. #11719917 | D4 | semidirect |
| 71. #88322 | C2×D4 | semidirect |
| 82. C4×C53 | AGL(1,ℤ/8) | semidirect |
| 93. C2×#127 | D53 | semidirect |
| 98. C53 | #3151 | semidirect |
| 174. C4 | #13133243 | semidirect |