Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
500 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#11719925 | C2 | semidirect |
| 4. #16810845 | C2 | direct (N × H) |
| 5. C2×C4⋊#88322 | C2 | semidirect |
| 6. C2×#13133140 | C2 | semidirect |
| 8. C2×C4×Q8×C53 | C2 | semidirect |
| 12. C2×#11719925 | C22 | semidirect |
| 21. C4⋊#88322 | C22 | semidirect |
| 22. #13133140 | C22 | semidirect |
| 26. C4×Q8×C53 | C22 | semidirect |
| 111. C2×C53 | #464 | semidirect |
| 119. C2×C4×Q8 | D53 | semidirect |
| 124. C53 | C2×#464 | semidirect |
| 137. C4×Q8 | C2×D53 | semidirect |
| 227. C2 | #16810845 | direct (N × H) |