Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
340 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 113 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×#13133151 | C2 | semidirect |
| 2. C2×#13133141 | C2 | semidirect |
| 4. C2×#13133127 | C2 | semidirect |
| 5. #16810530 | C2 | semidirect |
| 22. C2×SD16×C53 | C4 | semidirect |
| 86. C8×C53 | C22⋊C4 | semidirect |
| 120. C53 | #1973 | semidirect |
| 125. C2×SD16 | Dic53 | semidirect |
| 200. C8 | C22⋊Dic53 | semidirect |