Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
336 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#13133144 | C2 | semidirect |
| 4. C2×#13133143 | C2 | semidirect |
| 5. M16×Dic53 | C2 | semidirect |
| 6. C4×#11719919 | C2 | semidirect |
| 7. C2×#104×C53 | C2 | semidirect |
| 10. #13133215 | C4 | semidirect |
| 11. #13133213 | C4 | semidirect |
| 12. #13133206 | C4 | semidirect |
| 13. #13133204 | C4 | semidirect |
| 55. M16×C53 | D4 | semidirect |
| 73. #11719917 | D4 | semidirect |
| 140. Dic53 | #104 | semidirect |
| 153. C2×#104 | D53 | semidirect |
| 156. C53 | #1980 | semidirect |
| 206. M16 | C22⋊D53 | semidirect |