Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 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 | C22×C53 | C23×C4 |
| Fitting | C2×C4×D4×C53 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | C2×C4×D4 | D53 |
| hypocenter | C53 | #2328 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×D212 | C2 | semidirect |
| 3. #16810526 | C2 | semidirect |
| 4. #16810524 | C2 | semidirect |
| 5. #16810502 | C2 | semidirect |
| 6. #16810499 | C2 | semidirect |
| 7. #16810488 | C2 | semidirect |
| 8. #16810469 | C2 | semidirect |
| 9. C2×C4×D4×C53 | C2 | semidirect |
| 13. #13133213 | C4 | semidirect |
| 34. C2×D4×C53 | C2×C4 | semidirect |
| 43. C2×C22⋊D53 | C2×C4 | semidirect |
| 49. C2×D212 | C2×C4 | semidirect |
| 54. C42×C53 | D4 | semidirect |
| 60. C4×Dic53 | C2×C4 | semidirect |
| 126. C2×C4×D4 | D53 | semidirect |
| 133. C53 | #2328 | semidirect |
| 164. C2×D4 | C4×D53 | semidirect |
| 184. C42 | C22⋊D53 | semidirect |