Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D61 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C61×#424 | C2 |
| hypercenter | #424 | D61 |
| hypocenter | C61 | #2930 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ #424 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519785 | C2 | semidirect |
| 2. C22×#11758189 | C2 | semidirect |
| 4. #16839839 | C2 | semidirect |
| 5. #16839832 | C2 | semidirect |
| 6. #16839728 | C2 | semidirect |
| 7. #16839725 | C2 | semidirect |
| 8. #16839718 | C2 | semidirect |
| 9. C61×#424 | C2 | semidirect |
| 17. C2×#11758189 | C22 | semidirect |
| 19. C2×C8×D61 | C22 | semidirect |
| 26. #14519689 | C22 | semidirect |
| 27. #14519688 | C22 | semidirect |
| 28. C4×#92418 | C22 | semidirect |
| 32. C4⋊C8×C61 | C22 | semidirect |
| 58. C2×#92418 | D4 | semidirect |
| 119. #424 | D61 | semidirect |
| 123. C61 | #2930 | semidirect |
| 142. C4⋊C8 | C2×D61 | semidirect |