Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
344 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 344 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. D53⋊(C4⋊C8) | C2 | semidirect |
| 2. C2×#13133280 | C2 | semidirect |
| 4. C4×C4⋊#6157 | C2 | semidirect |
| 16. #13133206 | C4 | semidirect |
| 17. #13133205 | C4 | semidirect |
| 18. #13133204 | C4 | semidirect |
| 24. #124×C53 | C4 | semidirect |
| 128. C53 | #1983 | semidirect |
| 137. #124 | #6157 | semidirect |