Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13133139 | C2 | semidirect |
| 3. C2×#13133138 | C2 | semidirect |
| 4. C2×#13133137 | C2 | semidirect |
| 5. #16810519 | C2 | semidirect |
| 6. #16810377 | C2 | semidirect |
| 7. C2×#102×C53 | C2 | semidirect |
| 56. C4⋊Dic53 | D4 | semidirect |
| 151. C2×#102 | D53 | semidirect |
| 154. C53 | #2041 | semidirect |