Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
440 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 81 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. #16810346 | C2 | semidirect |
| 4. C53×#407 | C2 | semidirect |
| 15. C22⋊#88322 | C22 | semidirect |
| 19. C22⋊C8×C53 | C22 | semidirect |
| 63. C22×D53 | M16 | semidirect |
| 113. #407 | D53 | semidirect |
| 115. C53 | #1462 | semidirect |
| 130. C22⋊C8 | C2×D53 | semidirect |