Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1058 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 451 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D61 |
| commutator, socle | C22×C61 | C25 |
| Fitting | C61×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D61 |
| hypocenter | C61 | #3529 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16840512 | C2 | semidirect |
| 2. #16840506 | C2 | semidirect |
| 3. #16840501 | C2 | semidirect |
| 4. #16840311 | C2 | semidirect |
| 5. #16840291 | C2 | semidirect |
| 6. #16840268 | C2 | semidirect |
| 7. C61×H(3,𝔽4) | C2 | semidirect |
| 8. C2×#11758226 | C22 | semidirect |
| 10. C23×Dic61 | C22 | semidirect |
| 11. #14519775 | C22 | semidirect |
| 13. #14519770 | C22 | semidirect |
| 14. #14519769 | C22 | semidirect |
| 15. #14519765 | C22 | semidirect |
| 16. #14519761 | C22 | semidirect |
| 17. #14519759 | C22 | semidirect |
| 19. #14519754 | C22 | semidirect |
| 20. #14519753 | C22 | semidirect |
| 21. #14519750 | C22 | semidirect |
| 24. #14519746 | C22 | semidirect |
| 25. Q8×Dic61 | C22 | semidirect |
| 27. #14519737 | C22 | semidirect |
| 28. #14519733 | C22 | semidirect |
| 29. C42×D61 | C22 | semidirect |
| 100. H(3,𝔽4) | D61 | semidirect |
| 105. C61 | #3529 | semidirect |