Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
422 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 148 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 | C23×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | #123×C61 | C4 |
| hypercenter | #123 | #6923 |
| hypocenter | C61 | #2977 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16840794 | C2 | semidirect |
| 2. #16840792 | C2 | semidirect |
| 3. #16840790 | C2 | semidirect |
| 4. #16840789 | C2 | semidirect |
| 5. #16840786 | C2 | semidirect |
| 6. #16840736 | C2 | semidirect |
| 7. #16840735 | C2 | semidirect |
| 8. D61⋊(C22⋊C8) | C2 | semidirect |
| 10. C2×#11758213 | C22 | semidirect |
| 11. C2×#11758217 | C22 | semidirect |
| 14. C2×D61⋊C8 | C22 | semidirect |
| 15. C22×#92420 | C22 | semidirect |
| 16. #14519844 | C22 | semidirect |
| 17. C4⋊#92420 | C22 | semidirect |
| 20. #14519834 | C22 | semidirect |
| 23. C22⋊#92420 | C22 | semidirect |
| 24. #14519832 | C22 | semidirect |
| 25. C4×#92420 | C22 | semidirect |
| 142. C61 | #2977 | semidirect |