Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
292 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×#6157 |
| commutator | C4×C53 | C2×C42 |
| Frattini | C2×C4 | C22×#6157 |
| Fitting | #102×C53 | C4 |
| socle | C22×C53 | C4×D4 |
| hypercenter | #102 | #6157 |
| hypocenter | C53 | #1765 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #102 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16811588 | C2 | semidirect |
| 4. C2×#13133271 | C2 | semidirect |
| 5. #16811499 | C2 | semidirect |
| 6. #16811493 | C2 | semidirect |
| 9. #13133304 | C4 | semidirect |
| 16. #13133281 | C4 | semidirect |
| 23. #13133142 | C4 | semidirect |
| 24. #13133140 | C4 | semidirect |
| 25. #13133138 | C4 | semidirect |
| 26. #102×C53 | C4 | semidirect |
| 117. C53 | #1765 | semidirect |
| 133. #102 | #6157 | semidirect |