Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 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 |
|---|---|---|
| 1. #16811173 | C2 | semidirect |
| 2. #16810999 | C2 | semidirect |
| 3. #16810969 | C2 | semidirect |
| 4. #16810815 | C2 | semidirect |
| 5. #16810757 | C2 | semidirect |
| 6. #16810676 | C2 | semidirect |
| 7. C2×#127×C53 | C2 | semidirect |
| 9. C2×#11719922 | C22 | semidirect |
| 10. #13133217 | C22 | semidirect |
| 11. #13133214 | C22 | semidirect |
| 16. C4×D212 | C22 | semidirect |
| 17. C4⋊#88322 | C22 | semidirect |
| 18. #13133138 | C22 | semidirect |
| 20. C4×#88322 | C22 | semidirect |
| 73. C2×C4×C53 | D8 | semidirect |
| 114. C2×#127 | D53 | semidirect |
| 120. C53 | #3205 | semidirect |
| 193. C2×C4 | #11719922 | semidirect |