Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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×C8×D53 | C2 | semidirect |
| 3. C2×#13133138 | C2 | semidirect |
| 4. #16810480 | C2 | semidirect |
| 5. #16810386 | C2 | semidirect |
| 6. #16810385 | C2 | semidirect |
| 7. C2×#102×C53 | C2 | semidirect |
| 15. #13133188 | C4 | semidirect |
| 50. C2×C8×C53 | D4 | semidirect |
| 61. C2×#88322 | D4 | semidirect |
| 127. C2×D53 | #102 | semidirect |
| 149. C2×#102 | D53 | semidirect |
| 153. C53 | #1893 | semidirect |
| 200. C2×C8 | C22⋊D53 | semidirect |