Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1008 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 309 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. C22×#11719917 | C2 | semidirect |
| 2. C2×#13133176 | C2 | semidirect |
| 3. #16810628 | C2 | direct (N × H) |
| 4. C2×#13133138 | C2 | semidirect |
| 7. C2×#11719917 | C22 | semidirect |
| 8. C22×#88322 | C22 | semidirect |
| 10. #13133176 | C22 | semidirect |
| 11. C2×C4⋊Dic53 | C22 | semidirect |
| 14. #13133138 | C22 | semidirect |
| 19. C22×D4×C53 | C4 | semidirect |
| 35. C2×D4×C53 | C2×C4 | semidirect |
| 46. C4⋊Dic53 | C23 | semidirect |
| 50. C2×#88322 | C23 | semidirect |
| 95. C2×C53 | #418 | semidirect |
| 103. C53 | C2×#418 | semidirect |
| 108. C22×D4 | Dic53 | semidirect |
| 133. C2×D4 | C2×Dic53 | semidirect |
| 192. C2 | #16810628 | direct (N × H) |