Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 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 | C22 | C22×C22⋊D61 |
| commutator | C4×C61 | C23×C4 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#518 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #518 | D61 |
| hypocenter | C61 | #2948 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #518 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16840236 | C2 | semidirect |
| 3. #16839872 | C2 | semidirect |
| 4. C4×#11758199 | C2 | semidirect |
| 5. #16839798 | C2 | semidirect |
| 6. #16839767 | C2 | semidirect |
| 7. #16839766 | C2 | semidirect |
| 8. #16839718 | C2 | semidirect |
| 9. C61×#518 | C2 | semidirect |
| 11. C2×#11758199 | C4 | semidirect |
| 16. C4×D244 | C22 | semidirect |
| 20. #14519710 | C22 | semidirect |
| 21. #14519708 | C22 | semidirect |
| 22. #14519698 | C22 | semidirect |
| 23. #14519697 | C22 | semidirect |
| 24. #14519688 | C22 | semidirect |
| 25. C4×#92418 | C22 | semidirect |
| 28. C4×D4×C61 | C22 | semidirect |
| 36. C2×D4×C61 | C2×C4 | semidirect |
| 42. C2×D244 | C2×C4 | semidirect |
| 53. #11758199 | C2×C4 | semidirect |
| 54. #11758199 | C2×C4 | semidirect |
| 59. C2×#92418 | C2×C4 | semidirect |
| 111. #518 | D61 | semidirect |
| 118. C61 | #2948 | semidirect |
| 129. C4×D4 | C2×D61 | semidirect |
| 149. C2×D4 | C4×D61 | semidirect |