Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D244 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#405 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #405 | D61 |
| hypocenter | C61 | #3137 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16840390 | C2 | semidirect |
| 3. #16840131 | C2 | semidirect |
| 4. #16840122 | C2 | semidirect |
| 5. #16840117 | C2 | semidirect |
| 6. #16840113 | C2 | semidirect |
| 7. #16839772 | C2 | semidirect |
| 10. C2×#14519702 | C2 | semidirect |
| 11. C61×#405 | C2 | semidirect |
| 138. #405 | D61 | semidirect |
| 139. C61 | #3137 | semidirect |