Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. C2×#13133141 | C2 | semidirect |
| 5. #16810530 | C2 | semidirect |
| 6. #16810377 | C2 | semidirect |
| 7. C22×Q16×C53 | C2 | semidirect |
| 126. C22×Q16 | D53 | semidirect |
| 133. C53 | #2015 | semidirect |