Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D212 |
| commutator | C2×C4×C53 | C24 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C53×#407 | C2 |
| socle | C22×C53 | C22×D4 |
| hypercenter | #407 | D53 |
| hypocenter | C53 | #3193 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #407 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133196 | C2 | semidirect |
| 3. #16810959 | C2 | semidirect |
| 4. #16810937 | C2 | semidirect |
| 5. #16810869 | C2 | semidirect |
| 6. #16810776 | C2 | semidirect |
| 7. #16810764 | C2 | semidirect |
| 8. C53×#407 | C2 | semidirect |
| 9. C22×Dic106 | C22 | semidirect |
| 12. C2×#11719913 | C22 | semidirect |
| 16. #13133196 | C22 | semidirect |
| 22. C2×C4⋊Dic53 | C22 | semidirect |
| 26. #13133151 | C22 | semidirect |
| 27. #13133142 | C22 | semidirect |
| 28. #13133139 | C22 | semidirect |
| 30. C2×M16×C53 | C22 | semidirect |
| 32. C22⋊C8×C53 | C22 | semidirect |
| 137. #407 | D53 | semidirect |
| 138. C53 | #3193 | semidirect |
| 144. C2×M16 | C2×D53 | semidirect |
| 162. C22⋊C8 | C2×D53 | semidirect |