Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
270 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 2. C4×#11719917 | C2 | semidirect |
| 3. #16810362 | C2 | semidirect |
| 4. C4×M16×C53 | C2 | semidirect |
| 84. C4×M16 | D53 | semidirect |
| 86. C53 | #1525 | semidirect |