Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 117 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×#13133151 | C2 | semidirect |
| 4. #16810385 | C2 | semidirect |
| 5. C2×#107×C53 | C2 | semidirect |
| 10. C2×C8×D53 | C4 | semidirect |
| 68. C8×C53 | C22⋊C4 | semidirect |
| 83. C2×D53 | #107 | semidirect |
| 102. C2×#107 | D53 | semidirect |
| 105. C53 | #1808 | semidirect |
| 169. C8 | #11719921 | semidirect |