Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 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 |
| 3. C2×#13133139 | C2 | semidirect |
| 4. #16810525 | C2 | semidirect |
| 5. C2×C4×C8×C53 | C2 | semidirect |
| 9. C2×D424 | C4 | semidirect |
| 48. C2×C4×C53 | D8 | semidirect |
| 62. C8×C53 | C22⋊C4 | semidirect |
| 89. C2×C4×C8 | D53 | semidirect |
| 91. C53 | #1970 | semidirect |
| 140. C2×C4 | D424 | semidirect |
| 148. C8 | #11719921 | semidirect |