Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
996 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×#11719924 | C2 | semidirect |
| 3. #16810773 | C2 | direct (N × H) |
| 4. C2×#13133137 | C2 | semidirect |
| 5. C2×C22⋊#88322 | C2 | semidirect |
| 6. C2×C22⋊Q8×C53 | C2 | semidirect |
| 14. C2×#11719924 | C22 | semidirect |
| 15. C22×#88322 | C22 | semidirect |
| 16. #13133137 | C22 | semidirect |
| 17. C22⋊#88322 | C22 | semidirect |
| 18. C22×Q8×C53 | C22 | semidirect |
| 21. C22⋊Q8×C53 | C22 | semidirect |
| 23. C2×C4⋊C4×C53 | C22 | semidirect |
| 33. C2×Q8×C53 | C23 | semidirect |
| 51. C4⋊C4×C53 | C23 | semidirect |
| 55. C2×#88322 | C23 | semidirect |
| 58. C23×C53 | SD16 | semidirect |
| 92. C22×C53 | C2×SD16 | semidirect |
| 107. C2×C53 | #450 | semidirect |
| 114. C2×C22⋊Q8 | D53 | semidirect |
| 118. C53 | C2×#450 | semidirect |
| 120. C22×Q8 | C2×D53 | semidirect |
| 131. C22⋊Q8 | C2×D53 | semidirect |
| 133. C2×C4⋊C4 | C2×D53 | semidirect |
| 145. C2×Q8 | C22×D53 | semidirect |
| 166. C4⋊C4 | C22×D53 | semidirect |
| 178. C23 | #11719924 | semidirect |
| 209. C22 | C2×#11719924 | semidirect |
| 219. C2 | #16810773 | direct (N × H) |