Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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×#13133144 | C2 | semidirect |
| 3. C2×#13133143 | C2 | semidirect |
| 4. #16810622 | C2 | semidirect |
| 5. C2×#13133133 | C2 | semidirect |
| 6. #16810524 | C2 | semidirect |
| 7. C53×#417 | C2 | semidirect |
| 11. #13133263 | C4 | semidirect |
| 19. C2×#11719917 | C22 | semidirect |
| 21. C2×C4×Dic53 | C22 | semidirect |
| 28. C2×M16×C53 | C22 | semidirect |
| 29. C2×C4⋊C4×C53 | C22 | semidirect |
| 95. Q8×C53 | C22⋊C4 | semidirect |
| 99. D4×C53 | C22⋊C4 | semidirect |
| 124. D212 | C22⋊C4 | semidirect |
| 129. Dic106 | C22⋊C4 | semidirect |
| 170. #417 | D53 | semidirect |
| 173. C53 | #1792 | semidirect |
| 187. C2×M16 | C2×D53 | semidirect |
| 188. C2×C4⋊C4 | C2×D53 | semidirect |
| 263. Q8 | #11719921 | semidirect |
| 277. D4 | #11719921 | semidirect |