Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
568 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#6923 |
| commutator | C22×C61 | C2×C42 |
| Fitting | C2×C42×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C2×C42 | #6923 |
| hypocenter | C61 | #1434 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. (C2×#6923)⋊C4 | C4 | semidirect |
| 12. C2×C4×Dic61 | C4 | semidirect |
| 13. C2×C4×Dic61 | C4 | semidirect |
| 14. C2×C4×Dic61 | C4 | semidirect |
| 16. C2×C42×C61 | C4 | semidirect |
| 121. C61 | #1434 | semidirect |
| 130. C2×C42 | #6923 | semidirect |