Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 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×#13133281 | C2 | semidirect |
| 2. C4×#11719936 | C2 | semidirect |
| 3. C4×C4⋊#6157 | C2 | semidirect |
| 13. #13133217 | C4 | semidirect |
| 14. #13133204 | C4 | semidirect |
| 20. #127×C53 | C4 | semidirect |
| 37. #11719936 | D4 | semidirect |
| 80. C4×C53 | #104 | semidirect |
| 97. C53 | #1980 | semidirect |
| 101. #127 | #6157 | semidirect |
| 177. C4 | #13133281 | semidirect |