Finite Group DatabasebetaFinite Group DatabasebetaOrder 9536.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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×D149 |
| commutator, socle, cosocle | C22×C149 | C24 |
| Fitting | #126×C149 | C2 |
| prime radical | #18011884 | C2 |
| hypercenter | #126 | D149 |
| hypocenter | C149 | #542 |
| LCS | G ▷ C22×C149 ▷ C149 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #18011910 | C2 | semidirect |
| 2. #18011906 | C2 | semidirect |
| 3. #18011899 | C2 | semidirect |
| 4. #18011897 | C2 | semidirect |
| 5. #18011897 | C2 | semidirect |
| 6. #18011896 | C2 | semidirect |
| 7. #18011895 | C2 | semidirect |
| 8. #18011891 | C2 | semidirect |
| 9. #18011889 | C2 | semidirect |
| 10. #18011888 | C2 | semidirect |
| 12. C4×Dic298 | C2 | semidirect |
| 13. #18011871 | C2 | semidirect |
| 14. #18011869 | C2 | semidirect |
| 15. #126×C149 | C2 | semidirect |
| 103. C149 | #542 | semidirect |
| 107. #126 | D149 | semidirect |