Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
336 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 97 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. C4×C4⋊Dic53 | C2 | semidirect |
| 4. C4×M16×C53 | C2 | semidirect |
| 6. #13133217 | C4 | semidirect |
| 7. #13133214 | C4 | semidirect |
| 8. #13133205 | C4 | semidirect |
| 34. M16×C53 | D4 | semidirect |
| 81. C4×C53 | #104 | semidirect |
| 95. C4×M16 | D53 | semidirect |
| 97. C53 | #1980 | semidirect |
| 127. M16 | D212 | semidirect |
| 176. C4 | #13133143 | semidirect |