Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
584 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 147 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 | C53×#400 | C2 |
| hypercenter | #400 | D53 |
| hypocenter | C53 | #2564 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #400 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133197 | C2 | semidirect |
| 3. #16810558 | C2 | semidirect |
| 4. #16810543 | C2 | semidirect |
| 5. #16810536 | C2 | semidirect |
| 6. #16810510 | C2 | semidirect |
| 8. #16810497 | C2 | semidirect |
| 9. #16810482 | C2 | semidirect |
| 10. #95×D53 | C2 | semidirect |
| 11. C53×#400 | C2 | semidirect |
| 50. C2×D212 | Q8 | semidirect |
| 144. #400 | D53 | semidirect |
| 153. C53 | #2564 | semidirect |