Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
432 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13133139 | C2 | semidirect |
| 3. #16810483 | C2 | semidirect |
| 4. #16810386 | C2 | semidirect |
| 5. C23×C8×C53 | C2 | semidirect |
| 9. #13133191 | C4 | semidirect |
| 40. C2×C8×C53 | D4 | semidirect |
| 82. C22×C53 | #102 | semidirect |
| 107. C23×C8 | D53 | semidirect |
| 112. C53 | #1893 | semidirect |
| 147. C2×C8 | C22⋊D53 | semidirect |
| 194. C22 | #13133139 | semidirect |