Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
950 conjugacy classes of subgroups; only the 449 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 449 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D53 |
| commutator, socle | C22×C53 | C25 |
| Fitting | C53×#564 | C2 |
| hypercenter | #564 | D53 |
| hypocenter | C53 | #3567 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ #564 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811371 | C2 | semidirect |
| 2. #16811326 | C2 | semidirect |
| 3. #16811305 | C2 | semidirect |
| 4. #16811229 | C2 | semidirect |
| 5. #16811221 | C2 | semidirect |
| 6. #16811158 | C2 | semidirect |
| 7. C53×#564 | C2 | semidirect |
| 100. #564 | D53 | semidirect |
| 107. C53 | #3567 | semidirect |