Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16811338 | C2 | semidirect |
| 2. #16811028 | C2 | semidirect |
| 3. #16810948 | C2 | semidirect |
| 4. #16810914 | C2 | semidirect |
| 5. #16810859 | C2 | semidirect |
| 6. C4×D424 | C2 | semidirect |
| 7. #16810661 | C2 | semidirect |
| 8. C8×D4×C53 | C2 | semidirect |
| 94. C8×D4 | D53 | semidirect |
| 96. C53 | #3341 | semidirect |