Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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×#13133160 | C2 | semidirect |
| 2. #16811041 | C2 | semidirect |
| 3. #16810895 | C2 | semidirect |
| 5. #16810452 | C2 | semidirect |
| 6. #16810437 | C2 | semidirect |
| 7. C53×#362 | C2 | semidirect |
| 77. #362 | D53 | semidirect |
| 79. C53 | #2223 | semidirect |