Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
324 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 97 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×#13133224 | C2 | semidirect |
| 2. C2×#13133144 | C2 | semidirect |
| 3. C2×#13133144 | C2 | semidirect |
| 4. #16810590 | C2 | semidirect |
| 5. #16810388 | C2 | semidirect |
| 6. #16810377 | C2 | semidirect |
| 24. C2×Q16×C53 | C4 | semidirect |
| 25. C2×SD16×C53 | C4 | semidirect |
| 26. C2×SD16×C53 | C4 | semidirect |
| 27. C2×D8×C53 | C4 | semidirect |
| 138. C53 | #1876 | semidirect |
| 143. C2×Q16 | Dic53 | semidirect |
| 144. C2×SD16 | Dic53 | semidirect |
| 145. C2×SD16 | Dic53 | semidirect |
| 146. C2×D8 | Dic53 | semidirect |