Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. C42×Dic53 | C2 | semidirect |
| 4. #16810384 | C2 | semidirect |
| 5. C4×M16×C53 | C2 | semidirect |
| 7. C4×Dic106 | C4 | semidirect |
| 8. C4×D212 | C4 | semidirect |
| 15. #13133143 | C4 | direct (N × H) |
| 31. M16×C53 | C2×C4 | semidirect |
| 44. C4×Dic53 | C2×C4 | semidirect |
| 60. D212 | C42 | semidirect |
| 64. Dic106 | C42 | semidirect |
| 72. C4×C53 | #104 | semidirect |
| 86. C4×M16 | D53 | semidirect |
| 89. C53 | C4×#104 | semidirect |
| 115. M16 | C4×D53 | semidirect |
| 159. C4 | #13133143 | direct (N × H) |