Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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. #16810676 | C2 | semidirect |
| 3. #16810352 | C2 | semidirect |
| 4. C53×#431 | C2 | semidirect |
| 13. C4⋊#88322 | C22 | semidirect |
| 19. C4×C8×C53 | C22 | semidirect |
| 27. C2×D212 | C8 | semidirect |
| 90. #431 | D53 | semidirect |
| 92. C53 | #1478 | semidirect |
| 107. C4×C8 | C2×D53 | semidirect |