Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
336 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 109 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. #16810360 | C2 | direct (N × H) |
| 11. C22×Q8×C53 | C4 | semidirect |
| 15. C22⋊Q8×C53 | C4 | semidirect |
| 18. C2×C4⋊C4×C53 | C4 | semidirect |
| 23. C2×Q8×C53 | C2×C4 | semidirect |
| 40. C4⋊C4×C53 | C2×C4 | semidirect |
| 97. C2×C53 | #328 | semidirect |
| 105. C53 | C2×#328 | semidirect |
| 106. C22×Q8 | Dic53 | semidirect |
| 112. C22⋊Q8 | Dic53 | semidirect |
| 115. C2×C4⋊C4 | Dic53 | semidirect |
| 124. C2×Q8 | C2×Dic53 | semidirect |
| 143. C4⋊C4 | C2×Dic53 | semidirect |
| 197. C2 | #16810360 | direct (N × H) |