Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14519733 |
| commutator | C2×C4×C61 | C22×C4 |
| Frattini | C22×C4 | C22×D61 |
| Fitting | C61×#344 | C2 |
| socle | C2×C61 | #383 |
| hypercenter | #344 | D61 |
| hypocenter | C61 | #1841 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #344 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. #14519687 | C4 | semidirect |
| 13. C8×Dic61 | C4 | semidirect |
| 80. C61 | #1841 | semidirect |