Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 1. #16811173 | C2 | semidirect |
| 2. #16810920 | C2 | semidirect |
| 3. #16810908 | C2 | semidirect |
| 4. #16810903 | C2 | semidirect |
| 5. #16810874 | C2 | semidirect |
| 6. #16810871 | C2 | semidirect |
| 7. #16810835 | C2 | semidirect |
| 8. #16810823 | C2 | semidirect |
| 9. #16810818 | C2 | semidirect |
| 10. #16810647 | C2 | semidirect |
| 11. C53×#529 | C2 | semidirect |
| 143. #529 | D53 | semidirect |
| 153. C53 | #3251 | semidirect |