Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. M16×Dic53 | C2 | semidirect |
| 4. C42×Dic53 | C2 | semidirect |
| 5. #16810384 | C2 | semidirect |
| 6. #16810383 | C2 | semidirect |
| 9. Q8×Dic53 | C4 | semidirect |
| 11. D4×Dic53 | C4 | semidirect |
| 18. #13133144 | C4 | semidirect |
| 24. #104×C53 | C4 | semidirect |
| 39. M16×C53 | C2×C4 | semidirect |
| 42. C42×C53 | C2×C4 | semidirect |
| 52. C4×Dic53 | C2×C4 | semidirect |
| 56. #11719917 | C2×C4 | semidirect |
| 61. Q8×C53 | C42 | semidirect |
| 65. D4×C53 | C42 | semidirect |
| 101. Dic53 | #104 | direct (N × H) |
| 115. C53 | C4×#104 | semidirect |
| 130. #104 | Dic53 | direct (N × H) |
| 149. M16 | C2×Dic53 | semidirect |
| 165. C42 | C2×Dic53 | semidirect |
| 169. Q8 | C4×Dic53 | semidirect |
| 173. D4 | C4×Dic53 | semidirect |