Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
408 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 226 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | #6157 |
| commutator, hypocenter | C53 | C42×C8 |
| Frattini | C2×C4 | C22×#6157 |
| Fitting | C4×C8×C53 | C4 |
| socle | C22×C53 | C2×C42 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C4×#88324 | C4 | semidirect |
| 9. C8×#6157 | C4 | direct (N × H) |
| 12. C4×#88322 | C4 | semidirect |
| 13. C8×Dic53 | C4 | semidirect |
| 14. C4×C8×C53 | C4 | semidirect |
| 19. C4×#6157 | C8 | direct (N × H) |
| 37. #88324 | C42 | semidirect |
| 38. C8×C53 | C42 | semidirect |
| 39. #88322 | C42 | semidirect |
| 43. #6157 | C4×C8 | direct (N × H) |
| 44. C4×C53 | C4×C8 | semidirect |
| 46. Dic53 | C4×C8 | semidirect |
| 56. C53 | C42×C8 | semidirect |
| 66. C4×C8 | #6157 | direct (N × H) |
| 91. C8 | C4×#6157 | direct (N × H) |
| 98. C4 | C8×#6157 | direct (N × H) |