Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
670 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13133132 | C2 | semidirect |
| 2. #16810503 | C2 | semidirect |
| 4. C23×Dic53 | C22 | semidirect |
| 6. C2×C22⋊Dic53 | C22 | semidirect |
| 10. H(5,𝔽2)×C53 | C4 | semidirect |
| 43. C23×C53 | C22⋊C4 | semidirect |
| 54. C2×C4×C53 | C22⋊C4 | semidirect |
| 87. C53 | #1790 | semidirect |
| 89. H(5,𝔽2) | Dic53 | semidirect |
| 127. C23 | C22⋊Dic53 | semidirect |
| 144. C2×C4 | C22⋊Dic53 | semidirect |