Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
404 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C42×D53 |
| commutator | C4×C53 | C2×C42 |
| Frattini | C22×C4 | C22×D53 |
| Fitting | C53×H(3,ℤ/4) | C2 |
| socle | C2×C53 | C2×#95 |
| hypercenter | H(3,ℤ/4) | D53 |
| hypocenter | C53 | C2×H(3,ℤ/4) |
| LCS | G ▷ C4×C53 ▷ C53 | |
| UCS | C1 ◁ C4 ◁ H(3,ℤ/4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16810380 | C2 | semidirect |
| 4. #16810379 | C2 | semidirect |
| 5. C53×H(3,ℤ/4) | C2 | semidirect |
| 8. C2×#11719912 | C4 | semidirect |
| 11. C2×C8×D53 | C4 | semidirect |
| 14. #13133174 | C4 | semidirect |
| 18. C42×D53 | C4 | semidirect |
| 34. C2×C8×C53 | C2×C4 | semidirect |
| 37. C42×C53 | C2×C4 | semidirect |
| 43. C4×Dic53 | C2×C4 | semidirect |
| 45. C2×#88322 | C2×C4 | semidirect |
| 102. D53 | H(3,ℤ/4) | direct (N × H) |
| 107. H(3,ℤ/4) | D53 | direct (N × H) |
| 108. C53 | C2×H(3,ℤ/4) | semidirect |
| 142. C2×C8 | C4×D53 | semidirect |
| 151. C42 | C4×D53 | semidirect |