Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
164 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 51 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×#13133162 | C2 | semidirect |
| 2. C2×C16×D53 | C2 | semidirect |
| 3. #16810865 | C2 | semidirect |
| 5. #16810426 | C2 | semidirect |
| 6. #16810423 | C2 | semidirect |
| 7. C53×#367 | C2 | semidirect |
| 38. C16×C53 | D4 | semidirect |
| 63. C2×D53 | SD32 | semidirect |
| 80. #367 | D53 | semidirect |
| 83. C53 | #2217 | semidirect |
| 115. C16 | D212 | semidirect |