Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13133250 | C2 | semidirect |
| 2. C2×#13133248 | C2 | semidirect |
| 3. C2×#13133247 | C2 | semidirect |
| 5. C2×#13133215 | C2 | semidirect |
| 6. #16811016 | C2 | semidirect |
| 7. #16811014 | C2 | semidirect |
| 8. #16811001 | C2 | semidirect |
| 9. #16810994 | C2 | semidirect |
| 10. M16×Dic53 | C2 | semidirect |
| 11. C2×#137×C53 | C2 | semidirect |
| 70. M16×C53 | D4 | semidirect |
| 84. #11719917 | D4 | semidirect |
| 140. Dic53 | #137 | semidirect |
| 150. C2×#137 | D53 | semidirect |
| 158. C53 | #3152 | semidirect |
| 224. M16 | C22⋊D53 | semidirect |