Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
492 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 139 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×#393 | C2 |
| hypercenter | #393 | D53 |
| hypocenter | C53 | #2599 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×Dic53 | C2 | semidirect |
| 3. #16810555 | C2 | semidirect |
| 5. #16810542 | C2 | semidirect |
| 7. #16810510 | C2 | semidirect |
| 8. #16810506 | C2 | semidirect |
| 10. #16810490 | C2 | semidirect |
| 138. C53 | #2599 | semidirect |