Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
316 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. C2×#13133151 | C2 | semidirect |
| 2. C2×#13133149 | C2 | semidirect |
| 4. #16810386 | C2 | semidirect |
| 15. C2×M16×C53 | C4 | semidirect |
| 67. C8×C53 | C22⋊C4 | semidirect |
| 97. C53 | #1809 | semidirect |
| 101. C2×M16 | Dic53 | semidirect |
| 159. C8 | C22⋊Dic53 | semidirect |