Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#13133146 | C2 | semidirect |
| 4. #16810492 | C2 | semidirect |
| 5. #16810386 | C2 | semidirect |
| 6. #16810385 | C2 | semidirect |
| 11. D4×Dic53 | C4 | semidirect |
| 68. D4×C53 | C4⋊C4 | semidirect |
| 115. Dic53 | #102 | semidirect |
| 132. C53 | #1802 | semidirect |
| 193. D4 | #11719919 | semidirect |