Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
438 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 103 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×C4×D212 | C2 | semidirect |
| 3. C2×#13133139 | C2 | semidirect |
| 4. C2×#13133139 | C2 | semidirect |
| 5. #16810525 | C2 | semidirect |
| 6. #16810386 | C2 | semidirect |
| 7. C53×#336 | C2 | semidirect |
| 13. C2×D424 | C4 | semidirect |
| 42. C2×D212 | C2×C4 | semidirect |
| 53. C2×C8×C53 | C2×C4 | semidirect |
| 84. C2×C4×C53 | D8 | semidirect |
| 104. D212 | C22⋊C4 | semidirect |
| 153. #336 | D53 | semidirect |
| 154. C53 | #1879 | semidirect |
| 201. C2×C8 | C4×D53 | semidirect |
| 246. C2×C4 | D424 | semidirect |