Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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. #16811389 | C2 | semidirect |
| 3. #16810746 | C2 | semidirect |
| 4. #16810741 | C2 | semidirect |
| 5. #16810672 | C2 | semidirect |
| 6. C2×#13133145 | C2 | semidirect |
| 7. C4×M16×C53 | C2 | semidirect |
| 9. #13133250 | C4 | semidirect |
| 10. #13133245 | C4 | semidirect |
| 13. #13133223 | C22 | semidirect |
| 16. #13133153 | C22 | semidirect |
| 17. #13133145 | C22 | semidirect |
| 18. #13133145 | C22 | semidirect |
| 22. #97×C53 | C22 | semidirect |
| 23. C4×C8×C53 | C22 | semidirect |
| 44. Dic212 | C2×C4 | semidirect |
| 45. D424 | C2×C4 | semidirect |
| 46. #11719913 | C2×C4 | semidirect |
| 92. C4×M16 | D53 | semidirect |
| 93. C53 | #2956 | semidirect |
| 108. #97 | C2×D53 | semidirect |
| 109. C4×C8 | C2×D53 | semidirect |