Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
512 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C23×D61 |
| commutator | C22×C61 | C23×C4 |
| Fitting | C61×#381 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | #381 | D61 |
| hypocenter | C61 | #2313 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16839647 | C2 | semidirect |
| 3. #16839645 | C2 | semidirect |
| 10. C2×C4⋊Dic61 | C4 | semidirect |
| 92. C61 | #2313 | semidirect |