Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
958 conjugacy classes of subgroups; only the 449 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 449 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 | #3568 |
| 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. #16840481 | C2 | semidirect |
| 3. #16840443 | C2 | semidirect |
| 4. #16840376 | C2 | semidirect |
| 5. #16840347 | C2 | semidirect |
| 6. #16840291 | C2 | semidirect |
| 7. C61×H(3,𝔽4) | C2 | semidirect |
| 8. #14519775 | C22 | semidirect |
| 9. #14519771 | C22 | semidirect |
| 10. #14519770 | C22 | semidirect |
| 11. #14519770 | C22 | semidirect |
| 12. #14519770 | C22 | semidirect |
| 13. #14519770 | C22 | semidirect |
| 14. #14519769 | C22 | semidirect |
| 16. #14519763 | C22 | semidirect |
| 17. #14519759 | C22 | semidirect |
| 20. #14519754 | C22 | semidirect |
| 21. #14519754 | C22 | semidirect |
| 22. #14519754 | C22 | semidirect |
| 23. #14519753 | C22 | semidirect |
| 26. #14519746 | C22 | semidirect |
| 27. Q8×Dic61 | C22 | semidirect |
| 28. C4×Dic122 | C22 | semidirect |
| 31. #14519737 | C22 | semidirect |
| 32. #14519733 | C22 | semidirect |
| 33. #14519733 | C22 | semidirect |
| 34. C2×C22⋊Dic61 | C22 | semidirect |
| 35. C42×D61 | C22 | semidirect |
| 102. H(3,𝔽4) | D61 | semidirect |
| 108. C61 | #3568 | semidirect |