Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
278 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 85 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×#13133152 | C2 | semidirect |
| 5. #16810388 | C2 | semidirect |
| 6. #16810387 | C2 | semidirect |
| 7. C2×#108×C53 | C2 | semidirect |
| 99. C2×D53 | #108 | semidirect |
| 116. C2×#108 | D53 | semidirect |
| 121. C53 | #1855 | semidirect |