Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 129 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×#432 | C2 |
| socle | C22×C53 | C22×D4 |
| hypercenter | #432 | D53 |
| hypocenter | C53 | #3109 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #432 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811173 | C2 | semidirect |
| 2. C2×C4×D212 | C2 | semidirect |
| 3. #16810942 | C2 | semidirect |
| 4. #16810914 | C2 | semidirect |
| 5. #16810819 | C2 | semidirect |
| 6. #16810759 | C2 | semidirect |
| 7. #16810736 | C2 | semidirect |
| 8. C53×#432 | C2 | semidirect |
| 13. #13133217 | C22 | semidirect |
| 14. #13133214 | C22 | semidirect |
| 23. C4×D212 | C22 | semidirect |
| 26. #13133149 | C22 | semidirect |
| 28. #13133139 | C22 | semidirect |
| 30. C4⋊C8×C53 | C22 | semidirect |
| 32. #97×C53 | C22 | semidirect |
| 89. D212 | #41 | semidirect |
| 128. #432 | D53 | semidirect |
| 129. C53 | #3109 | semidirect |
| 149. C4⋊C8 | C2×D53 | semidirect |
| 153. #97 | C2×D53 | semidirect |