Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
856 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 218 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×#11719936 | C2 | semidirect |
| 2. C22×C4×#6157 | C2 | semidirect |
| 3. C2×#13133281 | C2 | direct (N × H) |
| 7. C2×#11719936 | C22 | semidirect |
| 10. C2×C4×#6157 | C22 | semidirect |
| 11. #13133281 | C22 | direct (N × H) |
| 14. C2×#11719947 | C4 | semidirect |
| 16. C22×Dic106 | C4 | semidirect |
| 20. C22×D4×C53 | C4 | semidirect |
| 26. C2×D4×C53 | C2×C4 | semidirect |
| 37. #11719947 | C2×C4 | semidirect |
| 44. C2×Dic106 | C2×C4 | semidirect |
| 47. C4×#6157 | C23 | semidirect |
| 49. #11719936 | C23 | semidirect |
| 59. D4×C53 | C22×C4 | semidirect |
| 75. Dic106 | C22×C4 | semidirect |
| 79. C22×C53 | #104 | semidirect |
| 93. C2×C53 | C2×#104 | semidirect |
| 101. C53 | C22×#104 | semidirect |
| 108. C22×D4 | #6157 | semidirect |
| 130. C2×D4 | C2×#6157 | semidirect |
| 158. D4 | C22×#6157 | semidirect |
| 180. C22 | #13133281 | direct (N × H) |
| 191. C2 | C2×#13133281 | direct (N × H) |