Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
446 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 119 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. #16811168 | C2 | semidirect |
| 2. #16811020 | C2 | semidirect |
| 3. #16810998 | C2 | semidirect |
| 4. #16810968 | C2 | semidirect |
| 5. #16810876 | C2 | semidirect |
| 6. #16810874 | C2 | semidirect |
| 7. #16810735 | C2 | semidirect |
| 8. #16810734 | C2 | semidirect |
| 9. #16810732 | C2 | semidirect |
| 10. M16×Dic53 | C2 | semidirect |
| 11. C53×#469 | C2 | semidirect |
| 94. C8×C53 | #41 | semidirect |
| 96. #88322 | #41 | semidirect |
| 125. #469 | D53 | semidirect |
| 130. C53 | #3184 | semidirect |
| 215. C8 | #11719947 | semidirect |