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×#11719913 | C2 | semidirect |
| 3. C2×#13133196 | C2 | semidirect |
| 4. #16810776 | C2 | direct (N × H) |
| 5. C2×#13133139 | C2 | semidirect |
| 6. C2×C22⋊C8×C53 | C2 | semidirect |
| 8. C22×Dic106 | C22 | semidirect |
| 15. C2×#11719913 | C22 | semidirect |
| 17. #13133196 | C22 | semidirect |
| 18. C2×C4⋊Dic53 | C22 | semidirect |
| 21. #13133139 | C22 | semidirect |
| 23. C22×C8×C53 | C22 | semidirect |
| 24. C22⋊C8×C53 | C22 | semidirect |
| 48. C2×Dic106 | C23 | semidirect |
| 50. C2×C8×C53 | C23 | semidirect |
| 53. C4⋊Dic53 | C23 | semidirect |
| 58. C23×C53 | SD16 | semidirect |
| 92. C22×C53 | C2×SD16 | semidirect |
| 107. C2×C53 | #450 | semidirect |
| 117. C2×C22⋊C8 | D53 | semidirect |
| 118. C53 | C2×#450 | semidirect |
| 129. C22×C8 | C2×D53 | semidirect |
| 136. C22⋊C8 | C2×D53 | semidirect |
| 163. C2×C8 | C22×D53 | semidirect |
| 178. C23 | #11719913 | semidirect |
| 209. C22 | C2×#11719913 | semidirect |
| 219. C2 | #16810776 | direct (N × H) |