Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
272 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 109 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. C22×#11719908 | C2 | semidirect |
| 2. C2×#13133151 | C2 | semidirect |
| 3. #16810424 | C2 | direct (N × H) |
| 7. C2×#11719908 | C22 | semidirect |
| 9. #13133151 | C22 | semidirect |
| 13. C2×D8×C53 | C4 | semidirect |
| 25. D8×C53 | C2×C4 | semidirect |
| 64. C2×C53 | #357 | semidirect |
| 72. C53 | C2×#357 | semidirect |
| 76. C2×D8 | Dic53 | semidirect |
| 93. D8 | C2×Dic53 | semidirect |
| 131. C2 | #16810424 | direct (N × H) |