Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
340 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 78 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×#13133286 | C2 | semidirect |
| 2. C2×#13133280 | C2 | semidirect |
| 4. C2×#13133271 | C2 | semidirect |
| 5. (C2×#6157)⋊Q8 | C2 | semidirect |
| 20. C2×#11719913 | C4 | semidirect |
| 21. C2×#11719923 | C4 | semidirect |
| 22. C2×#11719924 | C4 | semidirect |
| 26. C2×SD16×C53 | C4 | semidirect |
| 102. C8×C53 | C22⋊C4 | semidirect |
| 103. #88322 | C22⋊C4 | semidirect |
| 140. C53 | #1973 | semidirect |
| 148. C2×SD16 | #6157 | semidirect |
| 236. C8 | C22⋊#6157 | semidirect |