Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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 | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | D42×C61 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | D42 | D61 |
| hypocenter | C61 | #3294 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ D42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16840416 | C2 | semidirect |
| 2. #16840108 | C2 | semidirect |
| 3. #16840073 | C2 | semidirect |
| 4. #16840042 | C2 | semidirect |
| 5. #16839996 | C2 | semidirect |
| 6. #16839954 | C2 | semidirect |
| 7. #16839896 | C2 | semidirect |
| 8. C4×#11758199 | C2 | semidirect |
| 9. D4×#92418 | C2 | semidirect |
| 10. C2×#14519698 | C2 | semidirect |
| 11. D42×C61 | C2 | semidirect |
| 14. C2×#11758199 | C22 | semidirect |
| 15. C22×#92418 | C22 | semidirect |
| 16. #14519777 | C22 | semidirect |
| 19. #14519751 | C22 | semidirect |
| 20. C4×D244 | C22 | semidirect |
| 21. C2×C4⋊Dic61 | C22 | semidirect |
| 22. #14519710 | C22 | semidirect |
| 23. #14519710 | C22 | semidirect |
| 24. C4⋊#92418 | C22 | semidirect |
| 27. #14519698 | C22 | semidirect |
| 28. #14519698 | C22 | semidirect |
| 29. #14519698 | C22 | semidirect |
| 30. #14519697 | C22 | semidirect |
| 31. C22⋊#92418 | C22 | semidirect |
| 32. C4×#92418 | C22 | semidirect |
| 92. D4×C61 | D8 | semidirect |
| 93. D4×C61 | #41 | semidirect |
| 144. D42 | D61 | semidirect |
| 154. C61 | #3294 | semidirect |
| 239. D4 | #11758199 | semidirect |
| 240. D4 | #11758224 | semidirect |