Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
820 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 245 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D53 |
| commutator | C23×C53 | C24 |
| Frattini | C23 | C23×D53 |
| Fitting | C22×C22⋊C4×C53 | C2 |
| socle | C24×C53 | C23 |
| hypercenter | C22×C22⋊C4 | D53 |
| hypocenter | C53 | C2×#397 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C4⋊Dic53 | C2 | semidirect |
| 3. #16810548 | C2 | direct (N × H) |
| 4. C2×#13133124 | C2 | semidirect |
| 5. C2×#13133124 | C2 | semidirect |
| 10. C2×C4⋊Dic53 | C22 | semidirect |
| 13. #13133124 | C22 | semidirect |
| 14. #13133124 | C22 | semidirect |
| 96. C2×C53 | #397 | semidirect |
| 108. C53 | C2×#397 | semidirect |
| 197. C2 | #16810548 | direct (N × H) |