Finite Group DatabasebetaFinite Group DatabasebetaOrder 9664.
220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 220 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×D151 |
| commutator, socle, cosocle | C22×C151 | C24 |
| Fitting | C22⋊Q8×C151 | C2 |
| hypercenter | C22⋊Q8 | D151 |
| hypocenter | C151 | #562 |
| LCS | G ▷ C22×C151 ▷ C151 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #18012729 | C2 | semidirect |
| 2. #18012728 | C2 | semidirect |
| 3. #18012725 | C2 | semidirect |
| 4. #18012724 | C2 | semidirect |
| 5. #18012724 | C2 | semidirect |
| 6. #18012722 | C2 | semidirect |
| 7. #18012721 | C2 | semidirect |
| 8. #18012719 | C2 | semidirect |
| 9. #18012717 | C2 | semidirect |
| 10. #18012715 | C2 | semidirect |
| 11. #18012714 | C2 | semidirect |
| 12. #18012713 | C2 | semidirect |
| 13. #18012712 | C2 | semidirect |
| 14. #18012712 | C2 | semidirect |
| 15. C22⋊Q8×C151 | C2 | semidirect |
| 109. C151 | #562 | semidirect |
| 121. C22⋊Q8 | D151 | semidirect |