Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1018 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13133262 | C2 | semidirect |
| 2. C2×#13133186 | C2 | semidirect |
| 3. #16810809 | C2 | direct (N × H) |
| 4. C2×#13133132 | C2 | semidirect |
| 5. C2×#13133131 | C2 | semidirect |
| 6. C2×#120×C53 | C2 | semidirect |
| 9. #13133262 | C22 | semidirect |
| 17. #13133186 | C22 | semidirect |
| 19. C2×C22⋊Dic53 | C22 | semidirect |
| 20. #13133132 | C22 | semidirect |
| 21. #13133131 | C22 | semidirect |
| 22. C25×C53 | C22 | semidirect |
| 26. #120×C53 | C22 | semidirect |
| 28. C2×C22⋊C4×C53 | C22 | semidirect |
| 34. C24×C53 | D4 | semidirect |
| 36. C24×C53 | C23 | semidirect |
| 38. C23×D53 | D4 | semidirect |
| 43. C2×D4×C53 | D4 | semidirect |
| 46. C22×C4×C53 | D4 | semidirect |
| 56. C2×C22⋊D53 | D4 | semidirect |
| 60. C22×Dic53 | D4 | semidirect |
| 72. C22⋊C4×C53 | C23 | semidirect |
| 75. C22⋊Dic53 | C23 | semidirect |
| 96. C23×C53 | C2×D4 | semidirect |
| 103. C22×D53 | C2×D4 | semidirect |
| 111. C2×C4×C53 | C2×D4 | semidirect |
| 123. C2×Dic53 | C2×D4 | semidirect |
| 165. C2×C53 | B(4,𝔽2) | semidirect |
| 170. C2×#120 | D53 | semidirect |
| 174. C53 | C2×B(4,𝔽2) | semidirect |
| 175. C25 | C2×D53 | semidirect |
| 190. #120 | C2×D53 | semidirect |
| 194. C2×C22⋊C4 | C2×D53 | semidirect |
| 204. C24 | C22⋊D53 | semidirect |
| 206. C24 | C22×D53 | semidirect |
| 230. C2×D4 | C22⋊D53 | semidirect |
| 237. C22×C4 | C22⋊D53 | semidirect |
| 243. C22⋊C4 | C22×D53 | semidirect |
| 270. C23 | C2×C22⋊D53 | semidirect |
| 294. C2×C4 | C2×C22⋊D53 | semidirect |
| 333. C2 | #16810809 | direct (N × H) |