Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
192 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 57 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 | C23×C4 | C2×D53 |
| Fitting | C53×#407 | C2 |
| socle | C22×C53 | #95 |
| hypercenter | #407 | D53 |
| hypocenter | C53 | #1306 |
| LCS | G ▷ C23×C53 ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #407 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C22⋊#88322 | C4 | semidirect |
| 13. C22⋊C8×C53 | C4 | semidirect |
| 75. C53 | #1306 | semidirect |
| 83. C22⋊C8 | Dic53 | semidirect |