Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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. C4⋊C8×D53 | C2 | semidirect |
| 3. C4×#11719912 | C2 | semidirect |
| 4. #16810355 | C2 | semidirect |
| 5. #16810353 | C2 | semidirect |
| 6. D4⋊#88322 | C2 | semidirect |
| 7. C53×D4⋊C8 | C2 | semidirect |
| 113. D4⋊C8 | D53 | semidirect |
| 114. C53 | #1483 | semidirect |