Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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×D167 |
| commutator, socle, cosocle | C22×C167 | C24 |
| Fitting | #126×C167 | C2 |
| prime radical | C2×C22⋊D167 | C22 |
| hypercenter | #126 | D167 |
| hypocenter | C167 | #563 |
| LCS | G ▷ C22×C167 ▷ C167 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19128832 | C2 | semidirect |
| 2. #19128831 | C2 | semidirect |
| 3. #19128827 | C2 | semidirect |
| 4. #19128826 | C2 | semidirect |
| 5. #19128825 | C2 | semidirect |
| 6. #19128823 | C2 | semidirect |
| 7. #19128822 | C2 | semidirect |
| 11. #19128812 | C2 | semidirect |
| 12. #19128810 | C2 | semidirect |
| 13. #19128809 | C2 | semidirect |
| 14. #19128809 | C2 | semidirect |
| 15. #126×C167 | C2 | semidirect |
| 97. C167 | #563 | semidirect |
| 104. #126 | D167 | semidirect |