Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
756 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 198 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. #16811703 | C2 | semidirect |
| 2. #16811609 | C2 | semidirect |
| 3. D53⋊#100 | C2 | semidirect |
| 6. D53⋊M16 | C22 | semidirect |
| 7. #13133278 | C22 | semidirect |
| 8. #13133277 | C22 | semidirect |
| 82. C53 | #2888 | semidirect |