Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
274 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16810539 |
| commutator | C22×C4×C53 | C23 |
| Frattini | C22×C4 | C22×D53 |
| Fitting | C53×#421 | C2 |
| socle | C2×C53 | #394 |
| hypercenter | #421 | D53 |
| hypocenter | C53 | #2048 |
| LCS | G ▷ C22×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #421 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16810672 | C2 | semidirect |
| 3. #16810627 | C2 | semidirect |
| 4. #16810607 | C2 | semidirect |
| 5. C2×#13133133 | C2 | semidirect |
| 6. #16810393 | C2 | semidirect |
| 7. C53×#421 | C2 | semidirect |
| 113. #421 | D53 | semidirect |
| 118. C53 | #2048 | semidirect |