Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
388 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 101 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×#13133124 | C2 | semidirect |
| 3. #16810358 | C2 | direct (N × H) |
| 4. C2×C22⋊C8×C53 | C2 | semidirect |
| 5. C22×D212 | C4 | semidirect |
| 10. #13133191 | C4 | semidirect |
| 12. C2×C4⋊Dic53 | C4 | semidirect |
| 15. #13133124 | C22 | semidirect |
| 19. C22⋊C8×C53 | C22 | semidirect |
| 40. C2×D212 | C2×C4 | semidirect |
| 46. C4⋊Dic53 | C2×C4 | semidirect |
| 107. C2×C53 | #327 | semidirect |
| 113. C2×C22⋊C8 | D53 | semidirect |
| 116. C53 | C2×#327 | semidirect |
| 129. C22⋊C8 | C2×D53 | semidirect |
| 219. C2 | #16810358 | direct (N × H) |