Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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. #16811097 | C2 | semidirect |
| 3. #16810641 | C2 | semidirect |
| 4. #16810639 | C2 | semidirect |
| 5. C2×#13133133 | C2 | semidirect |
| 6. #16810379 | C2 | semidirect |
| 7. C53×H(3,ℤ/4) | C2 | semidirect |
| 11. #13133214 | C4 | semidirect |
| 12. #13133205 | C4 | semidirect |
| 38. C2×D212 | C2×C4 | semidirect |
| 42. C2×Dic106 | C2×C4 | semidirect |
| 50. C42×C53 | C2×C4 | semidirect |
| 51. C42×C53 | D4 | semidirect |
| 56. C4×Dic53 | D4 | semidirect |
| 123. H(3,ℤ/4) | D53 | semidirect |
| 124. C53 | #1911 | semidirect |
| 175. C42 | C4×D53 | semidirect |
| 176. C42 | D212 | semidirect |