Finite Group DatabasebetaFinite Group DatabasebetaOrder 9536.
238 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 97 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 | C4×D4×C149 | C2 |
| hypercenter | C4×D4 | D149 |
| hypocenter | C149 | #553 |
| LCS | G ▷ C22×C149 ▷ C149 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #18011905 | C2 | semidirect |
| 2. #18011904 | C2 | semidirect |
| 3. #18011901 | C2 | semidirect |
| 4. #18011896 | C2 | semidirect |
| 5. #18011894 | C2 | semidirect |
| 6. #18011885 | C2 | semidirect |
| 7. #18011884 | C2 | semidirect |
| 8. #18011883 | C2 | semidirect |
| 9. #18011883 | C2 | semidirect |
| 10. C4×C22⋊D149 | C2 | semidirect |
| 11. #18011871 | C2 | semidirect |
| 12. #18011871 | C2 | semidirect |
| 13. #18011868 | C2 | semidirect |
| 14. C2×#14558715 | C2 | semidirect |
| 15. C4×D4×C149 | C2 | semidirect |
| 109. C149 | #553 | semidirect |
| 123. C4×D4 | D149 | semidirect |