Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
186 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 186 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×#13133158 | C2 | semidirect |
| 2. #16810998 | C2 | semidirect |
| 3. D8×Dic53 | C2 | semidirect |
| 4. #16810441 | C2 | semidirect |
| 5. #16810425 | C2 | semidirect |
| 6. #16810424 | C2 | semidirect |
| 7. C2×D16×C53 | C2 | semidirect |
| 30. D8×C53 | D4 | semidirect |
| 74. Dic53 | D16 | semidirect |
| 83. C2×D16 | D53 | semidirect |
| 89. C53 | #2206 | semidirect |
| 115. D8 | C22⋊D53 | semidirect |