Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13133124 |
| commutator | C23×C53 | C42 |
| Frattini | C2×C42 | C2×D53 |
| Fitting | C53×#432 | C2 |
| socle | C22×C53 | #95 |
| hypercenter | #432 | D53 |
| hypocenter | C53 | #1308 |
| LCS | G ▷ C23×C53 ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #432 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 55. C53 | #1308 | semidirect |