Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
512 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 309 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. #16810661 | C2 | direct (N × H) |
| 3. C2×#13133151 | C2 | semidirect |
| 4. C2×#13133149 | C2 | semidirect |
| 11. #13133151 | C22 | semidirect |
| 12. #13133149 | C22 | semidirect |
| 14. C22×C8×C53 | C4 | semidirect |
| 28. C2×C8×C53 | C2×C4 | semidirect |
| 65. C2×C53 | #427 | semidirect |
| 73. C53 | C2×#427 | semidirect |
| 75. C22×C8 | Dic53 | semidirect |
| 96. C2×C8 | C2×Dic53 | semidirect |
| 132. C2 | #16810661 | direct (N × H) |