Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 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. #16811000 | C2 | semidirect |
| 3. C4×D424 | C2 | semidirect |
| 4. #16810425 | C2 | semidirect |
| 5. C53×C4⋊C16 | C2 | semidirect |
| 30. D424 | D4 | semidirect |
| 56. C4×C53 | D16 | semidirect |
| 69. C4⋊C16 | D53 | semidirect |
| 71. C53 | #2206 | semidirect |
| 123. C4 | D848 | semidirect |