Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 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×#408 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #408 | D61 |
| hypocenter | C61 | #3099 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C2×#41 ◁ #408 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16840245 | C2 | semidirect |
| 3. #16840104 | C2 | semidirect |
| 4. #16840093 | C2 | semidirect |
| 5. #16840087 | C2 | semidirect |
| 6. #16840081 | C2 | semidirect |
| 7. #16839804 | C2 | semidirect |
| 8. C2×#14519709 | C2 | semidirect |
| 9. #16839764 | C2 | semidirect |
| 10. #16839759 | C2 | semidirect |
| 11. C61×#408 | C2 | semidirect |
| 144. #408 | D61 | semidirect |
| 145. C61 | #3099 | semidirect |