Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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. #16810864 | C2 | semidirect |
| 4. #16810451 | C2 | semidirect |
| 5. #16810428 | C2 | semidirect |
| 6. #16810425 | C2 | semidirect |
| 7. C22×C16×C53 | C2 | semidirect |
| 39. C16×C53 | D4 | semidirect |
| 59. C22×C53 | SD32 | semidirect |
| 77. C22×C16 | D53 | semidirect |
| 83. C53 | #2217 | semidirect |
| 115. C16 | C22⋊D53 | semidirect |
| 138. C22 | #13133162 | semidirect |