Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1880 conjugacy classes of subgroups; only the 981 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 981 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D53 |
| commutator | C2×C53 | C22×C42 |
| Frattini | C23 | C23×D53 |
| Fitting | C24×C4×C53 | C2 |
| socle | C25×C53 | C22 |
| hypercenter | C24×C4 | D53 |
| hypocenter | C53 | C22×#95 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C25 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13133124 | C2 | direct (N × H) |
| 6. C23×Dic53 | C4 | semidirect |
| 8. #13133124 | C22 | direct (N × H) |
| 11. C23×C4×C53 | C4 | semidirect |
| 21. C22×C4×C53 | C2×C4 | semidirect |
| 26. C22×Dic53 | C2×C4 | semidirect |
| 41. C2×C4×C53 | C22×C4 | semidirect |
| 45. C2×Dic53 | C22×C4 | semidirect |
| 46. C22×C53 | #95 | semidirect |
| 60. C2×C53 | C2×#95 | semidirect |
| 69. C53 | C22×#95 | semidirect |
| 76. C23×C4 | Dic53 | semidirect |
| 92. C22×C4 | C2×Dic53 | semidirect |
| 111. C2×C4 | C22×Dic53 | semidirect |
| 112. C22 | #13133124 | direct (N × H) |
| 125. C2 | C2×#13133124 | direct (N × H) |