Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
396 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 157 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×C4×#88322 | C2 | semidirect |
| 3. C4×C4⋊Dic53 | C2 | semidirect |
| 4. #16810385 | C2 | semidirect |
| 9. #13133138 | C4 | direct (N × H) |
| 15. C4×D4×C53 | C4 | semidirect |
| 38. C4⋊Dic53 | C2×C4 | semidirect |
| 42. C2×#88322 | C2×C4 | semidirect |
| 51. D4×C53 | C42 | semidirect |
| 81. C4×C53 | #102 | semidirect |
| 98. C53 | C4×#102 | semidirect |
| 103. C4×D4 | Dic53 | semidirect |
| 144. D4 | C4×Dic53 | semidirect |
| 175. C4 | #13133138 | direct (N × H) |