Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×C22⋊D61 |
| commutator | C4×C61 | C25 |
| Frattini | C4 | C24×D61 |
| Fitting | C61×#585 | C2 |
| socle | C2×C61 | C23×D4 |
| hypercenter | #585 | D61 |
| hypocenter | C61 | #3586 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519824 | C2 | semidirect |
| 2. #16840577 | C2 | semidirect |
| 3. #16840573 | C2 | semidirect |
| 4. #16840560 | C2 | semidirect |
| 5. C2×#14519807 | C2 | semidirect |
| 6. #16840529 | C2 | semidirect |
| 7. C61×#585 | C2 | semidirect |
| 9. #14519824 | C22 | semidirect |
| 10. C2×#11758222 | C22 | semidirect |
| 12. C22×Dic122 | C22 | semidirect |
| 14. #14519808 | C22 | semidirect |
| 15. #14519807 | C22 | semidirect |
| 16. #14519807 | C22 | semidirect |
| 17. #14519803 | C22 | semidirect |
| 18. #14519802 | C22 | semidirect |
| 19. #14519797 | C22 | semidirect |
| 20. C2×#11758202 | C22 | semidirect |
| 21. C2×#11758200 | C22 | semidirect |
| 22. #14519784 | C22 | semidirect |
| 23. C2×#11758194 | C22 | semidirect |
| 25. 2−1+4×C61 | C22 | semidirect |
| 27. H(5,𝔽2)×C61 | C22 | semidirect |
| 113. #585 | D61 | semidirect |
| 120. C61 | #3586 | semidirect |
| 124. 2−1+4 | C2×D61 | semidirect |
| 126. H(5,𝔽2) | C2×D61 | semidirect |