Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
484 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13133248 | C2 | semidirect |
| 3. #16810845 | C2 | semidirect |
| 4. #16810833 | C2 | semidirect |
| 5. #16810823 | C2 | semidirect |
| 6. #16810647 | C2 | semidirect |
| 7. #16810622 | C2 | semidirect |
| 8. C2×C4×Q8×C53 | C2 | semidirect |
| 36. C2×Q8×C53 | D4 | semidirect |
| 111. C4×C53 | #137 | semidirect |
| 123. C2×C4×Q8 | D53 | semidirect |
| 129. C53 | #3037 | semidirect |
| 160. C2×Q8 | D212 | semidirect |
| 233. C4 | #13133248 | semidirect |