Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
388 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 129 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. C4×C4⋊Dic53 | C2 | semidirect |
| 4. #16810386 | C2 | semidirect |
| 5. C2×#97×C53 | C2 | semidirect |
| 9. C4×D212 | C4 | semidirect |
| 14. #13133139 | C4 | semidirect |
| 33. C2×C8×C53 | C2×C4 | semidirect |
| 40. C4⋊Dic53 | C2×C4 | semidirect |
| 64. D212 | C42 | semidirect |
| 93. C2×#97 | D53 | semidirect |
| 96. C53 | #1762 | semidirect |
| 124. C2×C8 | C4×D53 | semidirect |