Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
648 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 165 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×#11719922 | C2 | semidirect |
| 2. C2×#13133213 | C2 | semidirect |
| 3. C2×D4×Dic53 | C2 | semidirect |
| 4. #16810816 | C2 | direct (N × H) |
| 5. C2×#13133146 | C2 | semidirect |
| 6. C2×#13133139 | C2 | semidirect |
| 7. C2×#13133138 | C2 | semidirect |
| 8. C22×D8×C53 | C2 | semidirect |
| 14. C2×#11719922 | C22 | semidirect |
| 17. #13133213 | C22 | semidirect |
| 19. D4×Dic53 | C22 | semidirect |
| 23. #13133146 | C22 | semidirect |
| 24. #13133139 | C22 | semidirect |
| 25. #13133138 | C22 | semidirect |
| 29. C2×D8×C53 | C22 | semidirect |
| 39. C2×D4×C53 | D4 | semidirect |
| 85. D4×C53 | C2×D4 | semidirect |
| 96. C2×Dic53 | D8 | semidirect |
| 125. Dic53 | C2×D8 | semidirect |
| 129. C2×C53 | #459 | semidirect |
| 135. C22×D8 | D53 | semidirect |
| 142. C53 | C2×#459 | semidirect |
| 152. C2×D8 | C2×D53 | semidirect |
| 181. C2×D4 | C22⋊D53 | semidirect |
| 224. D4 | C2×C22⋊D53 | semidirect |
| 263. C2 | #16810816 | direct (N × H) |