Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
368 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. C2×#13133149 | C2 | semidirect |
| 3. C2×#13133139 | C2 | semidirect |
| 4. C2×#13133139 | C2 | semidirect |
| 5. #16810483 | C2 | semidirect |
| 6. #16810386 | C2 | semidirect |
| 7. C2×C22⋊C8×C53 | C2 | semidirect |
| 52. C2×C8×C53 | D4 | semidirect |
| 148. C2×C22⋊C8 | D53 | semidirect |
| 151. C53 | #2034 | semidirect |
| 196. C2×C8 | C22⋊D53 | semidirect |