Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
160 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C8 | C2×D61 |
| commutator | C2×C61 | C22×C16 |
| Frattini | C2×C8 | C22×D61 |
| Fitting | C2×C4×C8×C61 | C2 |
| socle | C22×C61 | C22×C8 |
| hypercenter | C2×C4×C8 | D61 |
| hypocenter | C61 | #2162 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4×C8 ◁ C2×C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4⋊#11758185 | C2 | semidirect |
| 3. C4×#11758185 | C2 | semidirect |
| 31. C2×C4×C61 | C16 | semidirect |
| 62. C61 | #2162 | semidirect |
| 89. C2×C4 | #11758185 | semidirect |