Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
460 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 213 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. #16810670 | C2 | direct (N × H) |
| 4. C2×#13133153 | C2 | semidirect |
| 5. C2×#13133152 | C2 | semidirect |
| 6. C2×#108×C53 | C2 | semidirect |
| 17. #13133153 | C22 | semidirect |
| 18. #13133152 | C22 | semidirect |
| 21. #108×C53 | C22 | semidirect |
| 84. C2×C53 | #430 | semidirect |
| 92. C2×#108 | D53 | semidirect |
| 93. C53 | C2×#430 | semidirect |
| 108. #108 | C2×D53 | semidirect |
| 171. C2 | #16810670 | direct (N × H) |