Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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. #16811197 | C2 | semidirect |
| 3. #16810639 | C2 | semidirect |
| 4. #16810632 | C2 | semidirect |
| 5. #16810597 | C2 | semidirect |
| 6. #16810395 | C2 | semidirect |
| 7. C2×#137×C53 | C2 | semidirect |
| 138. C2×#137 | D53 | semidirect |
| 144. C53 | #2009 | semidirect |