Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #16811224 | C2 | semidirect |
| 2. #16811024 | C2 | semidirect |
| 3. #16810998 | C2 | semidirect |
| 4. #16810986 | C2 | semidirect |
| 5. #16810875 | C2 | semidirect |
| 6. #16810860 | C2 | semidirect |
| 7. #16810856 | C2 | semidirect |
| 8. #16810733 | C2 | semidirect |
| 9. C4×D424 | C2 | semidirect |
| 10. #16810577 | C2 | semidirect |
| 11. C4×D8×C53 | C2 | semidirect |
| 133. C4×D8 | D53 | semidirect |
| 135. C53 | #3176 | semidirect |