Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 121 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. #16811022 | C2 | semidirect |
| 3. #16810980 | C2 | semidirect |
| 4. #16810958 | C2 | semidirect |
| 5. #16810953 | C2 | semidirect |
| 8. #16810927 | C2 | semidirect |
| 9. #16810920 | C2 | semidirect |
| 10. #16810676 | C2 | semidirect |
| 11. C2×#125×C53 | C2 | semidirect |
| 127. C2×#125 | D53 | semidirect |
| 137. C53 | #3232 | semidirect |