Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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×#13133163 | C2 | semidirect |
| 4. #16810428 | C2 | semidirect |
| 5. #16810427 | C2 | semidirect |
| 7. C2×Q32×C53 | C2 | semidirect |
| 70. C2×D53 | Q32 | semidirect |
| 85. C2×Q32 | D53 | semidirect |
| 90. C53 | #2188 | semidirect |