Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
912 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 290 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6157 |
| commutator | C2×C53 | C22×C42 |
| Fitting | C2×C22⋊C4×C53 | C4 |
| socle | C22×C53 | C23×C4 |
| hypercenter | C2×C22⋊C4 | #6157 |
| hypocenter | C53 | #2273 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22⋊C4×#6157 | C2 | semidirect |
| 3. C4×C22⋊#6157 | C2 | semidirect |
| 6. C2×C22⋊#6157 | C4 | semidirect |
| 9. C2×C4×#6157 | C22 | semidirect |
| 10. (C2×#6157)⋊C4 | C22 | semidirect |
| 13. C2×C22⋊Dic53 | C4 | semidirect |
| 14. C2×#11719921 | C4 | semidirect |
| 15. C22⋊C4×D53 | C4 | semidirect |
| 17. C2×C22⋊C4×C53 | C4 | semidirect |
| 26. C22×#6157 | C2×C4 | semidirect |
| 28. C22×C4×C53 | C2×C4 | semidirect |
| 29. C22×Dic53 | C2×C4 | semidirect |
| 31. C2×C4×D53 | C2×C4 | semidirect |
| 33. C22⋊#6157 | C2×C4 | semidirect |
| 34. C22⋊#6157 | C2×C4 | semidirect |
| 36. C22⋊C4×C53 | C2×C4 | semidirect |
| 37. C22⋊Dic53 | C2×C4 | semidirect |
| 38. #11719921 | C2×C4 | semidirect |
| 40. C23×C53 | C42 | semidirect |
| 48. C22×D53 | C42 | semidirect |
| 49. C22×D53 | C42 | semidirect |
| 97. C53 | #2273 | semidirect |
| 108. C2×C22⋊C4 | #6157 | semidirect |
| 125. C22×C4 | C2×#6157 | semidirect |
| 130. C22⋊C4 | C2×#6157 | semidirect |
| 146. C23 | C4×#6157 | semidirect |