Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
464 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 162 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×#13133305 | C2 | semidirect |
| 2. #16811669 | C2 | direct (N × H) |
| 3. C2×#13133287 | C2 | semidirect |
| 4. C2×#13133282 | C2 | semidirect |
| 5. C2×#13133271 | C2 | semidirect |
| 8. #13133305 | C22 | semidirect |
| 14. #13133287 | C22 | semidirect |
| 15. #13133282 | C22 | semidirect |
| 16. #13133271 | C22 | semidirect |
| 18. #13133240 | C4 | semidirect |
| 20. C2×#11719924 | C4 | semidirect |
| 21. C2×D424 | C4 | semidirect |
| 23. C2×Q16×C53 | C4 | semidirect |
| 44. Q16×C53 | C2×C4 | semidirect |
| 46. #11719924 | C2×C4 | semidirect |
| 48. D424 | C2×C4 | semidirect |
| 87. C2×C53 | #444 | semidirect |
| 98. C53 | C2×#444 | semidirect |
| 102. C2×Q16 | #6157 | semidirect |
| 126. Q16 | C2×#6157 | semidirect |
| 181. C2 | #16811669 | direct (N × H) |