Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
568 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D53 |
| commutator | C22×C53 | C23×C4 |
| Frattini | C23 | C23×D53 |
| Fitting | C4×C22⋊C4×C53 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | C4×C22⋊C4 | D53 |
| hypocenter | C53 | #2283 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16810490 | C2 | semidirect |
| 3. #16810487 | C2 | semidirect |
| 6. C4×#11719919 | C2 | semidirect |
| 8. #16810469 | C2 | semidirect |
| 14. C2×C4×Dic53 | C4 | semidirect |
| 109. C53 | #2283 | semidirect |