Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
416 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6923 |
| commutator, socle | C22×C61 | C2×C42 |
| Fitting | C2×M16×C61 | C4 |
| hypercenter | C2×M16 | #6923 |
| hypocenter | C61 | #1729 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. (C2×#6923)⋊C8 | C2 | semidirect |
| 7. C2×D61⋊C8 | C4 | semidirect |
| 9. C22×#92420 | C4 | semidirect |
| 16. C2×#11758194 | C4 | semidirect |
| 17. C2×#11758189 | C4 | semidirect |
| 21. C2×M16×C61 | C4 | semidirect |
| 107. C61 | #1729 | semidirect |
| 113. C2×M16 | #6923 | semidirect |