Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
230 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 230 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×#13133160 | C2 | semidirect |
| 2. C2×#13133158 | C2 | semidirect |
| 3. #16810859 | C2 | semidirect |
| 4. #16810427 | C2 | semidirect |
| 5. #16810424 | C2 | semidirect |
| 6. C22⋊#11719908 | C2 | semidirect |
| 7. C2×#135×C53 | C2 | semidirect |
| 33. Q16×C53 | D4 | semidirect |
| 36. D8×C53 | D4 | semidirect |
| 90. C2×#135 | D53 | semidirect |
| 97. C53 | #2186 | semidirect |
| 123. Q16 | C22⋊D53 | semidirect |
| 128. D8 | C22⋊D53 | semidirect |