Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
540 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6157 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C4×D4×C53 | C4 |
| hypercenter | C4×D4 | #6157 |
| hypocenter | C53 | #2319 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16811574 | C2 | semidirect |
| 3. #16811573 | C2 | semidirect |
| 4. #16811566 | C2 | semidirect |
| 5. #16811565 | C2 | semidirect |
| 6. C4×C4⋊#6157 | C2 | semidirect |
| 7. #16811559 | C2 | semidirect |
| 22. C4×D212 | C4 | semidirect |
| 23. D4×Dic53 | C4 | semidirect |
| 24. #13133179 | C4 | semidirect |
| 25. C4×C22⋊D53 | C4 | semidirect |
| 26. #13133177 | C4 | semidirect |
| 30. C4×D4×C53 | C4 | semidirect |
| 141. C53 | #2319 | semidirect |
| 149. C4×D4 | #6157 | semidirect |