Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
440 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 440 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×#390 | C2 |
| hypercenter | #390 | D53 |
| hypocenter | C53 | #2513 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16810551 | C2 | semidirect |
| 2. #16810551 | C2 | semidirect |
| 5. #16810519 | C2 | semidirect |
| 6. #16810517 | C2 | semidirect |
| 7. #16810511 | C2 | semidirect |
| 8. #16810489 | C2 | semidirect |
| 9. C4⋊C4×Dic53 | C2 | semidirect |
| 10. C4×#11719919 | C2 | semidirect |
| 148. C53 | #2513 | semidirect |