Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
324 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 70 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×#13133305 | C2 | semidirect |
| 2. C2×#13133282 | C2 | semidirect |
| 3. C2×#13133282 | C2 | semidirect |
| 4. #16811598 | C2 | semidirect |
| 5. #16811499 | C2 | semidirect |
| 6. (C2×#6157)⋊C8 | C2 | semidirect |
| 24. C2×#11719924 | C4 | semidirect |
| 25. C2×#11719924 | C4 | semidirect |
| 26. C2×D424 | C4 | semidirect |
| 28. C2×Q16×C53 | C4 | semidirect |
| 138. C53 | #1876 | semidirect |
| 143. C2×Q16 | #6157 | semidirect |