Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
336 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. C2×#13133145 | C2 | semidirect |
| 3. C4×#11719917 | C2 | semidirect |
| 4. C4×C4⋊C4×C53 | C2 | semidirect |
| 7. #13133217 | C4 | semidirect |
| 8. #13133214 | C4 | semidirect |
| 9. #13133205 | C4 | semidirect |
| 44. #11719917 | D4 | semidirect |
| 82. C4×C53 | #104 | semidirect |
| 96. C4×C4⋊C4 | D53 | semidirect |
| 97. C53 | #1980 | semidirect |
| 176. C4 | #13133145 | semidirect |