Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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×#13133150 | C2 | semidirect |
| 4. #16810521 | C2 | semidirect |
| 5. #16810385 | C2 | semidirect |
| 6. #16810378 | C2 | semidirect |
| 15. #13133138 | C4 | semidirect |
| 48. C4⋊Dic53 | C2×C4 | semidirect |
| 55. C2×#88322 | C2×C4 | semidirect |
| 67. D4×C53 | C4⋊C4 | semidirect |
| 131. C53 | #1862 | semidirect |
| 191. D4 | #11719919 | semidirect |