Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
346 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 346 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. #16810587 | C2 | semidirect |
| 3. #16810356 | C2 | semidirect |
| 4. C4×C22⋊C4×C53 | C2 | semidirect |
| 5. C22×D212 | C4 | semidirect |
| 10. #13133191 | C4 | semidirect |
| 12. C2×C4⋊Dic53 | C4 | semidirect |
| 15. C22⋊#88322 | C22 | semidirect |
| 19. #95×C53 | C22 | semidirect |
| 106. C4×C22⋊C4 | D53 | semidirect |
| 108. C53 | #1507 | semidirect |
| 123. #95 | C2×D53 | semidirect |