Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
422 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D61 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C61×#433 | C2 |
| hypercenter | #433 | D61 |
| hypocenter | C61 | #2977 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ #433 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16839835 | C2 | semidirect |
| 3. #16839832 | C2 | semidirect |
| 4. C8×D244 | C2 | semidirect |
| 5. #16839827 | C2 | semidirect |
| 6. #16839823 | C2 | semidirect |
| 7. #16839727 | C2 | semidirect |
| 8. C22⋊C8×D61 | C2 | semidirect |
| 9. C61×#433 | C2 | semidirect |
| 12. C2×#11758189 | C22 | semidirect |
| 15. C2×C8×D61 | C22 | semidirect |
| 22. C4⋊#92418 | C22 | semidirect |
| 26. #14519689 | C22 | semidirect |
| 27. #14519689 | C22 | semidirect |
| 28. #14519688 | C22 | semidirect |
| 29. C4×#92418 | C22 | semidirect |
| 31. C4⋊C8×C61 | C22 | semidirect |
| 33. #97×C61 | C22 | semidirect |
| 34. C4×C8×C61 | C22 | semidirect |
| 121. #433 | D61 | semidirect |
| 124. C61 | #2977 | semidirect |
| 139. C4⋊C8 | C2×D61 | semidirect |
| 147. #97 | C2×D61 | semidirect |
| 149. C4×C8 | C2×D61 | semidirect |