Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
380 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 97 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. #16810483 | C2 | semidirect |
| 4. #16810389 | C2 | semidirect |
| 5. C53×#380 | C2 | semidirect |
| 7. C22×C4×D53 | C4 | semidirect |
| 13. C2×#11719919 | C4 | semidirect |
| 16. C2×#11719921 | C4 | semidirect |
| 17. C2×C4×Dic53 | C4 | semidirect |
| 74. C22×D53 | C4⋊C4 | semidirect |
| 101. C2×Dic53 | C4⋊C4 | semidirect |
| 130. C4×C53 | #99 | semidirect |
| 149. #380 | D53 | semidirect |
| 151. C53 | #1799 | semidirect |
| 280. C4 | #13133131 | semidirect |