Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
422 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 205 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×#525 | C2 |
| hypercenter | #525 | D61 |
| hypocenter | C61 | #2977 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16839834 | C2 | semidirect |
| 2. D4×#92418 | C2 | semidirect |
| 3. #16839823 | C2 | semidirect |
| 4. #16839729 | C2 | semidirect |
| 5. C2×C22⋊#92418 | C2 | semidirect |
| 7. C2×#11758194 | C22 | semidirect |
| 9. C22×#92418 | C22 | semidirect |
| 10. C4⋊#92418 | C22 | semidirect |
| 14. C22⋊#92418 | C22 | semidirect |
| 15. #14519688 | C22 | semidirect |
| 16. C4×#92418 | C22 | semidirect |
| 96. C61 | #2977 | semidirect |