Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
292 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 109 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×C4 | C22×D53 |
| commutator | C22×C53 | C22×C8 |
| Fitting | C2×C4×C8×C53 | C2 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C2×C4×C8 | D53 |
| hypocenter | C53 | #1923 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133146 | C2 | semidirect |
| 5. #16810378 | C2 | semidirect |
| 6. #16810377 | C2 | semidirect |
| 7. C2×C4×C8×C53 | C2 | semidirect |
| 45. #11719921 | C8 | semidirect |
| 126. C2×C4×C8 | D53 | semidirect |
| 130. C53 | #1923 | semidirect |