Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. #16811173 | C2 | semidirect |
| 2. #16810913 | C2 | semidirect |
| 3. #16810910 | C2 | semidirect |
| 4. #16810874 | C2 | semidirect |
| 5. #16810818 | C2 | semidirect |
| 6. #16810815 | C2 | semidirect |
| 7. #16810647 | C2 | semidirect |
| 8. C53×#532 | C2 | semidirect |
| 122. #532 | D53 | semidirect |
| 129. C53 | #3253 | semidirect |