Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
912 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 325 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 | C2×C53 | C22×C42 |
| Fitting | C4×C22⋊C4×C53 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | C4×C22⋊C4 | D53 |
| hypocenter | C53 | #2273 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C22⋊C4×Dic53 | C2 | semidirect |
| 4. C4×#11719921 | C2 | semidirect |
| 5. C4×C22⋊Dic53 | C2 | semidirect |
| 6. #16810470 | C2 | semidirect |
| 7. C4×C22⋊C4×C53 | C2 | semidirect |
| 12. C2×#11719921 | C4 | semidirect |
| 16. C22⋊C4×D53 | C4 | semidirect |
| 17. C2×C4×Dic53 | C22 | semidirect |
| 18. C2×C4×Dic53 | C22 | semidirect |
| 19. #13133124 | C22 | semidirect |
| 20. #13133124 | C22 | semidirect |
| 23. C2×C42×C53 | C22 | semidirect |
| 24. #95×C53 | C22 | semidirect |
| 32. C22×C4×C53 | C2×C4 | semidirect |
| 37. C22×Dic53 | C2×C4 | semidirect |
| 42. C2×C4×D53 | C2×C4 | semidirect |
| 43. C22⋊C4×C53 | C2×C4 | semidirect |
| 45. C22⋊Dic53 | C2×C4 | semidirect |
| 46. #11719921 | C2×C4 | semidirect |
| 47. #11719921 | C2×C4 | semidirect |
| 48. #11719921 | C2×C4 | semidirect |
| 61. C22×D53 | C42 | semidirect |
| 112. C4×C22⋊C4 | D53 | semidirect |
| 113. C53 | #2273 | semidirect |
| 127. C2×C42 | C2×D53 | semidirect |
| 130. #95 | C2×D53 | semidirect |
| 145. C22×C4 | C4×D53 | semidirect |
| 153. C22⋊C4 | C4×D53 | semidirect |