Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
856 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 309 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×#11719917 | C2 | semidirect |
| 2. C22×C4×Dic53 | C2 | semidirect |
| 3. C2×#13133144 | C2 | direct (N × H) |
| 7. C2×#11719917 | C22 | semidirect |
| 10. C2×C4×Dic53 | C22 | semidirect |
| 11. #13133144 | C22 | direct (N × H) |
| 14. C2×#41×C53 | C4 | semidirect |
| 16. C22×Q8×C53 | C4 | semidirect |
| 18. C22×D4×C53 | C4 | semidirect |
| 26. #41×C53 | C2×C4 | semidirect |
| 29. C2×Q8×C53 | C2×C4 | semidirect |
| 33. C2×D4×C53 | C2×C4 | semidirect |
| 46. C4×Dic53 | C23 | semidirect |
| 48. #11719917 | C23 | semidirect |
| 57. Q8×C53 | C22×C4 | semidirect |
| 61. D4×C53 | C22×C4 | semidirect |
| 81. C22×C53 | #104 | semidirect |
| 95. C2×C53 | C2×#104 | semidirect |
| 101. C53 | C22×#104 | semidirect |
| 104. C2×#41 | Dic53 | semidirect |
| 106. C22×Q8 | Dic53 | semidirect |
| 108. C22×D4 | Dic53 | semidirect |
| 123. #41 | C2×Dic53 | semidirect |
| 126. C2×Q8 | C2×Dic53 | semidirect |
| 130. C2×D4 | C2×Dic53 | semidirect |
| 154. Q8 | C22×Dic53 | semidirect |
| 158. D4 | C22×Dic53 | semidirect |
| 178. C22 | #13133144 | direct (N × H) |
| 191. C2 | C2×#13133144 | direct (N × H) |