Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
320 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 320 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. C4×#11719917 | C2 | semidirect |
| 3. #16810469 | C2 | semidirect |
| 4. #16810382 | C2 | semidirect |
| 8. #13133144 | C4 | semidirect |
| 13. C4×Q8×C53 | C4 | semidirect |
| 15. C4×D4×C53 | C4 | semidirect |
| 40. C4×Dic53 | C2×C4 | semidirect |
| 42. #11719917 | C2×C4 | semidirect |
| 88. C53 | #1759 | semidirect |
| 91. C4×Q8 | Dic53 | semidirect |
| 93. C4×D4 | Dic53 | semidirect |