Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13133248 | C2 | semidirect |
| 3. #16811197 | C2 | semidirect |
| 4. #16810784 | C2 | semidirect |
| 5. #16810777 | C2 | semidirect |
| 6. #16810632 | C2 | semidirect |
| 7. #16810620 | C2 | semidirect |
| 8. #16810589 | C2 | semidirect |
| 9. C22×Q16×C53 | C2 | semidirect |
| 143. C22×Q16 | D53 | semidirect |
| 150. C53 | #3011 | semidirect |