Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
320 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 113 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. #16810469 | C2 | semidirect |
| 4. #16810384 | C2 | semidirect |
| 5. C4×M16×C53 | C2 | semidirect |
| 7. C4×Dic106 | C4 | semidirect |
| 8. C4×D212 | C4 | semidirect |
| 14. #13133143 | C4 | semidirect |
| 31. M16×C53 | C2×C4 | semidirect |
| 43. C4×Dic53 | C2×C4 | semidirect |
| 85. C4×M16 | D53 | semidirect |
| 88. C53 | #1759 | semidirect |
| 114. M16 | C4×D53 | semidirect |