Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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×D848 | C2 | semidirect |
| 2. C2×#13133156 | C2 | semidirect |
| 3. #16810860 | C2 | semidirect |
| 4. #16810423 | C2 | semidirect |
| 5. C53×#367 | C2 | semidirect |
| 26. C16×C53 | D4 | semidirect |
| 59. #367 | D53 | semidirect |
| 61. C53 | #2218 | semidirect |
| 83. C16 | D212 | semidirect |