Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1144 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 309 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D53 |
| commutator | C22×C53 | C23×C4 |
| Frattini | C23 | C23×D53 |
| Fitting | C2×#95×C53 | C2 |
| socle | C24×C53 | C23 |
| hypercenter | C2×#95 | D53 |
| hypocenter | C53 | C2×#381 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16810485 | C2 | direct (N × H) |
| 4. C2×#13133124 | C2 | semidirect |
| 5. C2×#13133124 | C2 | semidirect |
| 6. C2×#95×C53 | C2 | semidirect |
| 11. C22×C4×D53 | C4 | semidirect |
| 15. #13133124 | C22 | semidirect |
| 16. #13133124 | C22 | semidirect |
| 19. #95×C53 | C22 | semidirect |
| 43. C2×C4×D53 | C2×C4 | semidirect |
| 97. C2×C53 | #381 | semidirect |
| 109. C2×#95 | D53 | semidirect |
| 110. C53 | C2×#381 | semidirect |
| 123. #95 | C2×D53 | semidirect |
| 201. C2 | #16810485 | direct (N × H) |