Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 1. C2×#13133162 | C2 | semidirect |
| 3. C4×Dic212 | C2 | semidirect |
| 4. #16810425 | C2 | semidirect |
| 5. C53×C4⋊C16 | C2 | semidirect |
| 27. Dic212 | D4 | semidirect |
| 52. C4×C53 | SD32 | semidirect |
| 65. C4⋊C16 | D53 | semidirect |
| 67. C53 | #2207 | semidirect |
| 116. C4 | #13133162 | semidirect |