Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
412 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 137 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×#389 | C2 |
| hypercenter | #389 | D53 |
| hypocenter | C53 | #2494 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #389 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C53⋊#401 | C2 | semidirect |
| 3. #16810519 | C2 | semidirect |
| 5. #16810504 | C2 | semidirect |
| 6. #16810489 | C2 | semidirect |
| 9. C4⋊C4×Dic53 | C2 | semidirect |
| 11. C53×#389 | C2 | semidirect |
| 137. #389 | D53 | semidirect |
| 145. C53 | #2494 | semidirect |