Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
228 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 77 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 | C2×C4×C53 | C42 |
| Frattini | C23×C4 | C2×D53 |
| Fitting | C53×#380 | C2 |
| socle | C22×C53 | #95 |
| hypercenter | #380 | D53 |
| hypocenter | C53 | #1289 |
| LCS | G ▷ C2×C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C22×#88322 | C4 | semidirect |
| 9. #13133124 | C4 | semidirect |
| 13. #95×C53 | C4 | semidirect |
| 94. C53 | #1289 | semidirect |
| 104. #95 | Dic53 | semidirect |