Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
688 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D53 |
| commutator, socle | C23×C53 | C24 |
| Fitting | C22×C42×C53 | C2 |
| hypercenter | C22×C42 | D53 |
| hypocenter | C53 | #2854 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133200 | C2 | semidirect |
| 3. #16810525 | C2 | semidirect |
| 4. #16810521 | C2 | semidirect |
| 5. #16810514 | C2 | semidirect |
| 6. #16810502 | C2 | semidirect |
| 7. #16810483 | C2 | semidirect |
| 8. C22×C42×C53 | C2 | semidirect |
| 36. C22×C4×C53 | D4 | semidirect |
| 107. C4×C53 | #123 | semidirect |
| 120. C22×C42 | D53 | semidirect |
| 126. C53 | #2854 | semidirect |
| 160. C22×C4 | D212 | semidirect |
| 227. C4 | #13133200 | semidirect |