Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C2×#13133143 | C2 | semidirect |
| 3. #16810625 | C2 | semidirect |
| 4. #16810526 | C2 | semidirect |
| 5. C2×#100×C53 | C2 | semidirect |
| 8. #13133262 | C4 | semidirect |
| 13. C2×C4⋊Dic53 | C22 | semidirect |
| 15. C2×C4×Dic53 | C22 | semidirect |
| 20. C2×M16×C53 | C22 | semidirect |
| 80. D212 | C22⋊C4 | semidirect |
| 84. Dic106 | C22⋊C4 | semidirect |
| 116. C2×#100 | D53 | semidirect |
| 118. C53 | #1792 | semidirect |
| 127. C2×M16 | C2×D53 | semidirect |