Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
512 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 3. #16810660 | C2 | direct (N × H) |
| 4. C2×#13133151 | C2 | semidirect |
| 5. C2×#13133148 | C2 | semidirect |
| 6. C2×#107×C53 | C2 | semidirect |
| 9. C2×C8×D53 | C4 | semidirect |
| 16. #13133151 | C22 | semidirect |
| 17. #13133148 | C22 | semidirect |
| 20. #107×C53 | C22 | semidirect |
| 40. C8×D53 | C2×C4 | semidirect |
| 76. C2×C53 | #427 | semidirect |
| 85. C2×#107 | D53 | semidirect |
| 87. C53 | C2×#427 | semidirect |
| 100. #107 | C2×D53 | semidirect |
| 157. C2 | #16810660 | direct (N × H) |