Finite Group DatabasebetaFinite Group DatabasebetaOrder 9664.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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, prime radical | #120×C151 | C2 |
| hypercenter | #120 | D151 |
| hypocenter | C151 | #551 |
| LCS | G ▷ C22×C151 ▷ C151 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #18012732 | C2 | semidirect |
| 2. #18012726 | C2 | semidirect |
| 3. #18012720 | C2 | semidirect |
| 4. #18012720 | C2 | semidirect |
| 5. #18012716 | C2 | semidirect |
| 6. D4×Dic151 | C2 | semidirect |
| 7. #18012695 | C2 | semidirect |
| 8. C2×C22⋊Dic151 | C2 | semidirect |
| 10. C2×Dic302 | C22 | semidirect |
| 13. C22×Dic151 | C22 | semidirect |
| 14. C4⋊Dic151 | C22 | semidirect |
| 15. Dic151⋊C4 | C22 | semidirect |
| 16. Dic151⋊C4 | C22 | semidirect |
| 17. Dic151⋊C4 | C22 | semidirect |
| 22. C22⋊Dic151 | C22 | semidirect |
| 23. C22⋊Dic151 | C22 | semidirect |
| 24. C4×Dic151 | C22 | semidirect |
| 25. C4×Dic151 | C22 | semidirect |
| 68. C151 | #551 | semidirect |