Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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. C22×#11719924 | C2 | semidirect |
| 3. C2×#13133136 | C2 | semidirect |
| 4. C2×#13133133 | C2 | semidirect |
| 5. #16810590 | C2 | semidirect |
| 6. #16810387 | C2 | semidirect |
| 7. C2×#137×C53 | C2 | semidirect |
| 128. C2×#137 | D53 | semidirect |
| 135. C53 | #2019 | semidirect |