Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
774 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 255 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 | C2×#131×C53 | C2 |
| hypercenter | C2×#131 | D53 |
| hypocenter | C53 | #2880 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13133224 | C2 | semidirect |
| 3. #16810591 | C2 | semidirect |
| 4. #16810589 | C2 | semidirect |
| 5. #16810586 | C2 | semidirect |
| 6. C2×#13133129 | C2 | semidirect |
| 7. C2×#131×C53 | C2 | semidirect |
| 17. C2×#11719917 | C22 | semidirect |
| 18. C22×#88322 | C22 | semidirect |
| 21. #13133129 | C22 | semidirect |
| 22. #13133129 | C22 | semidirect |
| 23. #13133129 | C22 | semidirect |
| 26. C2×M16×C53 | C22 | semidirect |
| 27. C22×C8×C53 | C22 | semidirect |
| 96. C2×D53 | #131 | semidirect |
| 111. C2×#131 | D53 | semidirect |
| 116. C53 | #2880 | semidirect |
| 129. C2×M16 | C2×D53 | semidirect |
| 131. C22×C8 | C2×D53 | semidirect |