Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D212 |
| commutator | C2×C4×C53 | C24 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C53×#436 | C2 |
| socle | C22×C53 | C22×D4 |
| hypercenter | #436 | D53 |
| hypocenter | C53 | #3354 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ #436 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16811338 | C2 | semidirect |
| 2. #16811277 | C2 | semidirect |
| 3. #16811021 | C2 | semidirect |
| 4. #16810948 | C2 | semidirect |
| 5. #16810942 | C2 | semidirect |
| 6. #16810914 | C2 | semidirect |
| 7. #16810904 | C2 | semidirect |
| 8. #16810876 | C2 | semidirect |
| 9. C4×D424 | C2 | semidirect |
| 10. #16810665 | C2 | semidirect |
| 11. C53×#436 | C2 | semidirect |
| 101. C8×C53 | #41 | semidirect |
| 137. #436 | D53 | semidirect |
| 139. C53 | #3354 | semidirect |
| 229. C8 | #11719947 | semidirect |