Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
412 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 78 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×D53⋊M16 | C2 | semidirect |
| 2. C2×#13133279 | C2 | semidirect |
| 3. #16811565 | C2 | semidirect |
| 4. #16811496 | C2 | semidirect |
| 17. #13133192 | C4 | semidirect |
| 18. #13133191 | C4 | semidirect |
| 21. #13133188 | C4 | semidirect |
| 24. #121×C53 | C4 | semidirect |
| 54. D53⋊C8 | D4 | semidirect |
| 147. C53 | #1895 | semidirect |
| 160. #121 | #6157 | semidirect |