Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
536 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 3. #16810666 | C2 | direct (N × H) |
| 4. C2×#13133150 | C2 | semidirect |
| 5. C2×#13133148 | C2 | semidirect |
| 8. C2×#11719917 | C4 | semidirect |
| 15. #13133150 | C22 | semidirect |
| 16. #13133148 | C22 | semidirect |
| 45. #11719917 | C2×C4 | semidirect |
| 46. C2×#88322 | C2×C4 | semidirect |
| 69. #88322 | C22×C4 | semidirect |
| 87. C2×C53 | #428 | semidirect |
| 97. C53 | C2×#428 | semidirect |
| 177. C2 | #16810666 | direct (N × H) |