Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
568 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 568 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×#393 | C2 |
| hypercenter | #393 | D53 |
| hypocenter | C53 | #2398 |
| 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. #16810565 | C2 | semidirect |
| 4. #16810550 | C2 | semidirect |
| 5. #16810548 | C2 | semidirect |
| 7. #16810534 | C2 | semidirect |
| 8. C22⋊C4×Dic53 | C2 | semidirect |
| 9. #16810470 | C2 | semidirect |
| 10. #16810468 | C2 | semidirect |
| 11. C53×#393 | C2 | semidirect |
| 146. #393 | D53 | semidirect |
| 150. C53 | #2398 | semidirect |