Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
260 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 77 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×#13133136 | C2 | semidirect |
| 2. #16810420 | C2 | direct (N × H) |
| 6. #13133136 | C22 | semidirect |
| 72. C2×C53 | #355 | semidirect |
| 77. C53 | C2×#355 | semidirect |
| 145. C2 | #16810420 | direct (N × H) |