Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
788 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 202 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×#13133296 | C2 | semidirect |
| 2. #16811604 | C2 | direct (N × H) |
| 3. C2×#13133276 | C2 | semidirect |
| 6. #13133296 | C22 | semidirect |
| 10. #13133276 | C22 | semidirect |
| 14. C2×#11719949 | C4 | semidirect |
| 16. C22×D212 | C4 | semidirect |
| 18. C22×C4×D53 | C4 | semidirect |
| 20. C22×Q8×C53 | C4 | semidirect |
| 26. C2×Q8×C53 | C2×C4 | semidirect |
| 39. C2×D212 | C2×C4 | semidirect |
| 45. C2×C4×D53 | C2×C4 | semidirect |
| 108. C2×C53 | #410 | semidirect |
| 117. C53 | C2×#410 | semidirect |
| 123. C22×Q8 | #6157 | semidirect |
| 142. C2×Q8 | C2×#6157 | semidirect |
| 223. C2 | #16811604 | direct (N × H) |