Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
618 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#13133145 | C2 | semidirect |
| 3. #16810587 | C2 | semidirect |
| 4. C4×C22⋊C4×C53 | C2 | semidirect |
| 8. C2×#11719945 | C4 | semidirect |
| 10. C22×Dic106 | C4 | semidirect |
| 11. C22×D212 | C4 | semidirect |
| 14. C2×#11719917 | C22 | semidirect |
| 20. C2×C42×C53 | C22 | semidirect |
| 84. D212 | C22⋊C4 | semidirect |
| 89. Dic106 | C22⋊C4 | semidirect |
| 99. C22×C53 | #104 | semidirect |
| 123. C4×C22⋊C4 | D53 | semidirect |
| 124. C53 | #1789 | semidirect |
| 137. C2×C42 | C2×D53 | semidirect |
| 223. C22 | #13133145 | semidirect |