Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
452 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D53 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C53×#431 | C2 |
| hypercenter | #431 | D53 |
| hypocenter | C53 | #2975 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #431 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16810702 | C2 | semidirect |
| 3. #16810700 | C2 | semidirect |
| 4. #16810676 | C2 | semidirect |
| 5. #16810585 | C2 | semidirect |
| 6. C53×#431 | C2 | semidirect |
| 9. C2×#11719912 | C22 | semidirect |
| 16. C4⋊#88322 | C22 | semidirect |
| 18. #13133129 | C22 | semidirect |
| 19. C4×#88322 | C22 | semidirect |
| 21. C4⋊C8×C53 | C22 | semidirect |
| 23. C4×C8×C53 | C22 | semidirect |
| 53. C2×C4×C53 | M16 | semidirect |
| 93. #431 | D53 | semidirect |
| 95. C53 | #2975 | semidirect |
| 107. C4⋊C8 | C2×D53 | semidirect |
| 112. C4×C8 | C2×D53 | semidirect |
| 148. C2×C4 | #11719912 | semidirect |