Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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×#13133160 | C2 | semidirect |
| 2. C2×D848 | C2 | semidirect |
| 3. C2×#13133158 | C2 | semidirect |
| 4. #16811008 | C2 | semidirect |
| 5. #16810998 | C2 | semidirect |
| 6. #16810398 | C2 | semidirect |
| 7. C2×SD32×C53 | C2 | semidirect |
| 42. C16×C53 | D4 | semidirect |
| 43. #11719908 | D4 | semidirect |
| 80. C2×SD32 | D53 | semidirect |
| 86. C53 | #2250 | semidirect |
| 122. C16 | C22⋊D53 | semidirect |