Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
274 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 81 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 | semidirect |
| 11. C22×Q8×C53 | C4 | semidirect |
| 15. C22⋊Q8×C53 | C4 | semidirect |
| 18. C2×C4⋊C4×C53 | C4 | semidirect |
| 98. C53 | #1511 | semidirect |
| 99. C22×Q8 | Dic53 | semidirect |
| 104. C22⋊Q8 | Dic53 | semidirect |
| 107. C2×C4⋊C4 | Dic53 | semidirect |