Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
196 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
| 2. C2×#13133161 | C2 | semidirect |
| 3. C2×#13133160 | C2 | semidirect |
| 4. #16811001 | C2 | semidirect |
| 6. C16×Dic53 | C2 | semidirect |
| 7. C2×SD32×C53 | C2 | semidirect |
| 42. C16×C53 | D4 | semidirect |
| 43. #11719908 | D4 | semidirect |
| 71. Dic53 | SD32 | semidirect |
| 80. C2×SD32 | D53 | semidirect |
| 84. C53 | #2248 | semidirect |
| 120. C16 | C22⋊D53 | semidirect |