Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 141 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. #16810985 | C2 | semidirect |
| 3. #16810975 | C2 | semidirect |
| 4. #16810971 | C2 | semidirect |
| 5. #16810622 | C2 | semidirect |
| 6. C4×#11719917 | C2 | semidirect |
| 7. C2×C4⋊Q8×C53 | C2 | semidirect |
| 102. C2×C4⋊Q8 | D53 | semidirect |
| 108. C53 | #3141 | semidirect |