Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
3464 conjugacy classes of subgroups; only the 429 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 429 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 | C22×C53 | C23×C4 |
| Frattini | C23 | C23×D53 |
| Fitting | C22×C22⋊C4×C53 | C2 |
| socle | C24×C53 | C23 |
| hypercenter | C22×C22⋊C4 | D53 |
| hypocenter | C53 | C2×#379 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C22⋊Dic53 | C2 | semidirect |
| 3. C22×#11719921 | C2 | semidirect |
| 4. #16810478 | C2 | direct (N × H) |
| 5. C22×C22⋊C4×C53 | C2 | semidirect |
| 9. C24×D53 | C4 | semidirect |
| 12. C23×Dic53 | C22 | semidirect |
| 14. C2×C22⋊Dic53 | C22 | semidirect |
| 16. C2×#11719921 | C22 | semidirect |
| 18. C23×C4×C53 | C22 | semidirect |
| 20. C2×C22⋊C4×C53 | C22 | semidirect |
| 38. C23×D53 | C2×C4 | semidirect |
| 43. C22×C4×C53 | C23 | semidirect |
| 46. C22×Dic53 | C23 | semidirect |
| 54. C23×C53 | C22⋊C4 | semidirect |
| 75. C22×D53 | C22⋊C4 | semidirect |
| 90. C22×C53 | C2×C22⋊C4 | semidirect |
| 103. C2×D53 | C2×C22⋊C4 | semidirect |
| 108. C2×C53 | #379 | semidirect |
| 117. C22×C22⋊C4 | D53 | semidirect |
| 119. C53 | C2×#379 | semidirect |
| 128. C23×C4 | C2×D53 | semidirect |
| 134. C2×C22⋊C4 | C2×D53 | semidirect |
| 160. C22×C4 | C22×D53 | semidirect |
| 183. C23 | #11719921 | semidirect |
| 211. C22 | C2×#11719921 | semidirect |
| 222. C2 | #16810478 | direct (N × H) |