Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
448 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D53 |
| commutator | C2×C4×C53 | C24 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C53×#460 | C2 |
| socle | C22×C53 | C22×D4 |
| hypercenter | #460 | D53 |
| hypocenter | C53 | #3324 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #460 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811346 | C2 | semidirect |
| 3. #16810969 | C2 | semidirect |
| 4. #16810945 | C2 | semidirect |
| 5. #16810904 | C2 | semidirect |
| 6. #16810866 | C2 | semidirect |
| 7. #16810772 | C2 | semidirect |
| 8. C4×#11719924 | C2 | semidirect |
| 9. #16810700 | C2 | semidirect |
| 10. #16810626 | C2 | semidirect |
| 11. C53×#460 | C2 | semidirect |
| 15. C2×#11719912 | C22 | semidirect |
| 16. #13133217 | C22 | semidirect |
| 19. #13133193 | C22 | semidirect |
| 26. #13133175 | C22 | semidirect |
| 27. #13133151 | C22 | semidirect |
| 28. #13133148 | C22 | semidirect |
| 29. #13133141 | C22 | semidirect |
| 31. #13133138 | C22 | semidirect |
| 32. #13133138 | C22 | semidirect |
| 34. #13133129 | C22 | semidirect |
| 35. C4×#88322 | C22 | semidirect |
| 36. C2×SD16×C53 | C22 | semidirect |
| 38. C4×Q8×C53 | C22 | semidirect |
| 39. C4⋊C8×C53 | C22 | semidirect |
| 40. #102×C53 | C22 | semidirect |
| 142. #460 | D53 | semidirect |
| 147. C53 | #3324 | semidirect |
| 151. C2×SD16 | C2×D53 | semidirect |
| 162. C4×Q8 | C2×D53 | semidirect |
| 168. C4⋊C8 | C2×D53 | semidirect |
| 174. #102 | C2×D53 | semidirect |