Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 101 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. #16810647 | C2 | semidirect |
| 3. C2×#13133145 | C2 | semidirect |
| 4. C43×C53 | C2 | semidirect |
| 7. #13133217 | C4 | semidirect |
| 8. #13133214 | C4 | semidirect |
| 9. #13133205 | C4 | semidirect |
| 32. C42×C53 | D4 | semidirect |
| 63. C4×C53 | #104 | semidirect |
| 76. C43 | D53 | semidirect |
| 77. C53 | #1962 | semidirect |
| 109. C42 | D212 | semidirect |
| 137. C4 | #13133145 | semidirect |