Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
422 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D53 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C53×#433 | C2 |
| hypercenter | #433 | D53 |
| hypocenter | C53 | #2977 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #433 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16810696 | C2 | semidirect |
| 3. #16810693 | C2 | semidirect |
| 4. C8×D212 | C2 | semidirect |
| 5. #16810688 | C2 | semidirect |
| 6. #16810684 | C2 | semidirect |
| 7. #16810588 | C2 | semidirect |
| 8. C22⋊C8×D53 | C2 | semidirect |
| 9. C53×#433 | C2 | semidirect |
| 12. C2×#11719912 | C22 | semidirect |
| 15. C2×C8×D53 | C22 | semidirect |
| 22. C4⋊#88322 | C22 | semidirect |
| 26. #13133129 | C22 | semidirect |
| 27. #13133129 | C22 | semidirect |
| 28. #13133128 | C22 | semidirect |
| 29. C4×#88322 | C22 | semidirect |
| 31. C4⋊C8×C53 | C22 | semidirect |
| 33. #97×C53 | C22 | semidirect |
| 34. C4×C8×C53 | C22 | semidirect |
| 121. #433 | D53 | semidirect |
| 124. C53 | #2977 | semidirect |
| 139. C4⋊C8 | C2×D53 | semidirect |
| 147. #97 | C2×D53 | semidirect |
| 149. C4×C8 | C2×D53 | semidirect |