Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
688 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 152 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 | #120×C61 | C4 |
| hypercenter | #120 | #6923 |
| hypocenter | C61 | #2375 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16840714 | C2 | semidirect |
| 2. #16840712 | C2 | semidirect |
| 3. #16840710 | C2 | semidirect |
| 4. #16840703 | C2 | semidirect |
| 6. C23×#6923 | C22 | semidirect |
| 7. C2×C4⋊#6923 | C22 | semidirect |
| 10. C2×C22⋊#6923 | C22 | semidirect |
| 11. C2×C4×#6923 | C22 | semidirect |
| 12. (C2×#6923)⋊C4 | C22 | semidirect |
| 15. #14519747 | C4 | semidirect |
| 16. #14519746 | C4 | semidirect |
| 17. #14519745 | C4 | semidirect |
| 19. #120×C61 | C4 | semidirect |
| 20. C24×C61 | C2×C4 | semidirect |
| 23. C23×D61 | C2×C4 | semidirect |
| 41. C22⋊C4×C61 | C2×C4 | semidirect |
| 42. C22⋊Dic61 | C2×C4 | semidirect |
| 43. #11758198 | C2×C4 | semidirect |
| 106. C61 | #2375 | semidirect |
| 113. #120 | #6923 | semidirect |
| 126. C24 | C2×#6923 | semidirect |
| 143. C22⋊C4 | C2×#6923 | semidirect |