Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
452 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 158 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. #16811703 | C2 | semidirect |
| 2. #16811669 | C2 | semidirect |
| 3. #16811667 | C2 | semidirect |
| 4. D53⋊#108 | C2 | semidirect |
| 5. #16811622 | C2 | semidirect |
| 6. #16811586 | C2 | semidirect |
| 9. #13133305 | C22 | semidirect |
| 14. #13133288 | C22 | semidirect |
| 15. #13133287 | C22 | semidirect |
| 16. #13133282 | C22 | semidirect |
| 17. #13133271 | C22 | semidirect |
| 18. C8×#6157 | C22 | semidirect |
| 20. #13133240 | C4 | semidirect |
| 21. #13133240 | C4 | semidirect |
| 24. C2×#11719924 | C4 | semidirect |
| 25. C2×D424 | C4 | semidirect |
| 27. C2×Q16×C53 | C4 | semidirect |
| 109. C53 | #2957 | semidirect |
| 115. C2×Q16 | #6157 | semidirect |