Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
482 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#13133239 | C2 | semidirect |
| 2. C2×Q16×D53 | C2 | semidirect |
| 3. #16811283 | C2 | semidirect |
| 4. #16811008 | C2 | semidirect |
| 5. #16810860 | C2 | semidirect |
| 6. #16810848 | C2 | semidirect |
| 7. #16810783 | C2 | semidirect |
| 8. #16810763 | C2 | semidirect |
| 9. #16810717 | C2 | semidirect |
| 10. C8×C22⋊D53 | C2 | semidirect |
| 11. C53×#467 | C2 | semidirect |
| 76. Dic212 | D4 | semidirect |
| 120. C2×D53 | #135 | semidirect |
| 141. #467 | D53 | semidirect |
| 148. C53 | #3285 | semidirect |