Finite Group DatabasebetaFinite Group DatabasebetaOrder 9664.
212 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 95 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×D151 |
| commutator, socle, cosocle | C22×C151 | C24 |
| Fitting | #126×C151 | C2 |
| prime radical | C2×C22⋊D151 | C22 |
| hypercenter | #126 | D151 |
| hypocenter | C151 | #556 |
| LCS | G ▷ C22×C151 ▷ C151 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #18012738 | C2 | semidirect |
| 2. #18012734 | C2 | semidirect |
| 3. #18012734 | C2 | semidirect |
| 4. #18012732 | C2 | semidirect |
| 7. #18012717 | C2 | semidirect |
| 8. #18012716 | C2 | semidirect |
| 9. C4×Dic302 | C2 | semidirect |
| 10. #18012704 | C2 | semidirect |
| 11. #18012704 | C2 | semidirect |
| 13. #18012696 | C2 | semidirect |
| 14. #18012695 | C2 | semidirect |
| 15. #126×C151 | C2 | semidirect |
| 97. C151 | #556 | semidirect |
| 103. #126 | D151 | semidirect |