Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
996 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 197 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. C22×#11719923 | C2 | semidirect |
| 2. C2×#13133196 | C2 | semidirect |
| 3. #16810774 | C2 | direct (N × H) |
| 4. C2×#13133138 | C2 | semidirect |
| 5. C2×C22⋊#88322 | C2 | semidirect |
| 7. C22×Dic106 | C22 | semidirect |
| 9. C2×#11719923 | C22 | semidirect |
| 10. C22×#88322 | C22 | semidirect |
| 12. #13133196 | C22 | semidirect |
| 13. C2×C4⋊Dic53 | C22 | semidirect |
| 16. #13133138 | C22 | semidirect |
| 17. C22⋊#88322 | C22 | semidirect |
| 48. C2×Dic106 | C23 | semidirect |
| 52. C4⋊Dic53 | C23 | semidirect |
| 55. C2×#88322 | C23 | semidirect |
| 66. C23×C53 | SD16 | semidirect |
| 97. C22×C53 | C2×SD16 | semidirect |
| 108. C2×C53 | #450 | semidirect |
| 118. C53 | C2×#450 | semidirect |
| 178. C23 | #11719923 | semidirect |
| 209. C22 | C2×#11719923 | semidirect |
| 219. C2 | #16810774 | direct (N × H) |