Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
262 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13133186 |
| commutator | C2×C4×C53 | C22×C4 |
| Frattini | C22×C4 | C22×D53 |
| Fitting | C53×#568 | C2 |
| socle | C2×C53 | #385 |
| hypercenter | #568 | D53 |
| hypocenter | C53 | #1861 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #568 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16810671 | C2 | semidirect |
| 2. #16810646 | C2 | semidirect |
| 5. #16810394 | C2 | semidirect |
| 6. #16810384 | C2 | semidirect |
| 15. #13133144 | C4 | semidirect |
| 16. #13133144 | C4 | semidirect |
| 105. C53 | #1861 | semidirect |