Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
612 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 1. C2×#13133276 | C2 | semidirect |
| 2. #16811566 | C2 | semidirect |
| 9. C22×D212 | C4 | semidirect |
| 11. C22×C4×D53 | C4 | semidirect |
| 13. C22×Q8×C53 | C4 | semidirect |
| 79. C53 | #1782 | semidirect |
| 82. C22×Q8 | #6157 | semidirect |