Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
456 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 160 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. #16811663 | C2 | semidirect |
| 3. Q16×#6157 | C2 | semidirect |
| 20. C2×Dic212 | C4 | semidirect |
| 21. C2×#11719925 | C4 | semidirect |
| 22. Q16×D53 | C4 | semidirect |
| 23. Q16×D53 | C4 | semidirect |
| 27. C2×Q16×C53 | C4 | semidirect |
| 108. C53 | #2950 | semidirect |
| 116. C2×Q16 | #6157 | semidirect |