Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 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 | C2 | D4×D212 |
| commutator | C2×C4×C53 | C24 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C53×#443 | C2 |
| socle | C2×C53 | D42 |
| hypercenter | #443 | D53 |
| hypocenter | C53 | #3293 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #443 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811440 | C2 | semidirect |
| 2. #16811437 | C2 | semidirect |
| 3. #16811003 | C2 | semidirect |
| 4. #16810899 | C2 | semidirect |
| 5. #16810898 | C2 | semidirect |
| 6. #16810807 | C2 | semidirect |
| 7. #16810741 | C2 | semidirect |
| 8. C53×#443 | C2 | semidirect |
| 107. #443 | D53 | semidirect |
| 108. C53 | #3293 | semidirect |