Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 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×#13133161 | C2 | semidirect |
| 3. #16811007 | C2 | semidirect |
| 4. C4⋊#11719908 | C2 | semidirect |
| 5. #16810426 | C2 | semidirect |
| 6. #16810423 | C2 | semidirect |
| 7. C4×D8×C53 | C2 | semidirect |
| 80. C4×D8 | D53 | semidirect |
| 84. C53 | #2210 | semidirect |