Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 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×C4⋊#88322 | C2 | semidirect |
| 3. C2×#13133138 | C2 | semidirect |
| 4. C2×#13133137 | C2 | semidirect |
| 5. #16810525 | C2 | semidirect |
| 6. #16810385 | C2 | semidirect |
| 7. C53×#390 | C2 | semidirect |
| 88. C2×C4×C53 | D8 | semidirect |
| 148. #390 | D53 | semidirect |
| 150. C53 | #2054 | semidirect |
| 238. C2×C4 | #11719922 | semidirect |