Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1048 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1048 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×#11719922 | C2 | semidirect |
| 2. C2×#13133191 | C2 | semidirect |
| 3. #16810757 | C2 | direct (N × H) |
| 4. C2×#13133138 | C2 | semidirect |
| 5. C2×C22⋊#88322 | C2 | semidirect |
| 6. C23×D4×C53 | C2 | semidirect |
| 7. C22×D212 | C22 | semidirect |
| 10. C2×#11719922 | C22 | semidirect |
| 11. C22×#88322 | C22 | semidirect |
| 13. #13133191 | C22 | semidirect |
| 14. C2×C4⋊Dic53 | C22 | semidirect |
| 16. #13133138 | C22 | semidirect |
| 17. C22⋊#88322 | C22 | semidirect |
| 23. C22×D4×C53 | C22 | semidirect |
| 38. C2×D4×C53 | D4 | semidirect |
| 50. C2×D212 | C23 | semidirect |
| 54. C4⋊Dic53 | C23 | semidirect |
| 56. C2×#88322 | C23 | semidirect |
| 67. C23×C53 | D8 | semidirect |
| 77. D4×C53 | C2×D4 | semidirect |
| 101. C22×C53 | C2×D8 | semidirect |
| 115. C2×C53 | #447 | semidirect |
| 120. C23×D4 | D53 | semidirect |
| 126. C53 | C2×#447 | semidirect |
| 134. C22×D4 | C2×D53 | semidirect |
| 163. C2×D4 | C22⋊D53 | semidirect |
| 191. C23 | #11719922 | semidirect |
| 200. D4 | C2×C22⋊D53 | semidirect |
| 225. C22 | C2×#11719922 | semidirect |
| 235. C2 | #16810757 | direct (N × H) |