Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
300 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22⋊D53 |
| commutator | C4×C53 | C2×C42 |
| Frattini | C22×C4 | C22×D53 |
| Fitting | C53×#405 | C2 |
| socle | C22×C53 | C4×D4 |
| hypercenter | #405 | D53 |
| hypocenter | C53 | #1764 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×C8×Dic53 | C2 | semidirect |
| 5. #16810387 | C2 | semidirect |
| 6. #16810382 | C2 | semidirect |
| 7. C53×#405 | C2 | semidirect |
| 10. #13133223 | C4 | semidirect |
| 16. #13133143 | C4 | semidirect |
| 17. #13133140 | C4 | semidirect |
| 18. #13133137 | C4 | semidirect |
| 102. #405 | D53 | semidirect |
| 106. C53 | #1764 | semidirect |