Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1212 conjugacy classes of subgroups; only the 509 normal subgroups are shown.
This group has 1212 conjugacy classes of subgroups — too many to draw. Only its 509 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D61 |
| commutator, socle | C22×C61 | C25 |
| Frattini | C22 | C24×D61 |
| Fitting | C22×C42×C61 | C2 |
| hypercenter | C22×C42 | D61 |
| hypocenter | C61 | #3444 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C42 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16840319 | C2 | semidirect |
| 2. #16840312 | C2 | semidirect |
| 3. #16840296 | C2 | semidirect |
| 4. #16840273 | C2 | semidirect |
| 5. C4×#11758222 | C2 | semidirect |
| 6. C22×C42×C61 | C2 | semidirect |
| 8. #14519777 | C22 | semidirect |
| 9. #14519774 | C22 | semidirect |
| 10. #14519771 | C22 | semidirect |
| 11. #14519769 | C22 | semidirect |
| 12. #14519765 | C22 | semidirect |
| 17. C4×Dic122 | C22 | semidirect |
| 18. C4×D244 | C22 | semidirect |
| 21. #14519734 | C22 | semidirect |
| 22. C42×D61 | C22 | semidirect |
| 55. C2×C4×C61 | #41 | semidirect |
| 82. C22×C42 | D61 | semidirect |
| 83. C61 | #3444 | semidirect |
| 137. C2×C4 | #11758222 | semidirect |