Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
390 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 390 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×#13133133 | C2 | semidirect |
| 3. #16810587 | C2 | semidirect |
| 4. #16810391 | C2 | semidirect |
| 5. C22×M16×C53 | C2 | semidirect |
| 43. M16×C53 | D4 | semidirect |
| 93. C22×C53 | #100 | semidirect |
| 114. C22×M16 | D53 | semidirect |
| 119. C53 | #1900 | semidirect |
| 159. M16 | C22⋊D53 | semidirect |
| 211. C22 | #13133133 | semidirect |