Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16811027 | C2 | semidirect |
| 3. #16810957 | C2 | semidirect |
| 4. #16810956 | C2 | semidirect |
| 5. #16810916 | C2 | semidirect |
| 6. #16810861 | C2 | semidirect |
| 7. Q16×Dic53 | C2 | semidirect |
| 9. C2×#13133151 | C2 | semidirect |
| 10. #107×D53 | C2 | semidirect |
| 11. C53×#467 | C2 | semidirect |
| 79. C22⋊D53 | Q16 | semidirect |
| 123. #467 | D53 | semidirect |
| 128. C53 | #3338 | semidirect |