Finite Group DatabasebetaFinite Group DatabasebetaOrder 9664.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 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 | #120×C151 | C2 |
| hypercenter | #120 | D151 |
| hypocenter | C151 | #538 |
| 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. #18012732 | C2 | semidirect |
| 3. #18012726 | C2 | semidirect |
| 4. #18012725 | C2 | semidirect |
| 5. #18012721 | C2 | semidirect |
| 6. #18012720 | C2 | semidirect |
| 7. #18012716 | C2 | semidirect |
| 8. #18012711 | C2 | semidirect |
| 9. #18012711 | C2 | semidirect |
| 10. #18012710 | C2 | semidirect |
| 11. #18012708 | C2 | semidirect |
| 12. D4×Dic151 | C2 | semidirect |
| 13. (C22⋊D151)⋊C4 | C2 | semidirect |
| 14. C2×C22⋊Dic151 | C2 | semidirect |
| 15. #120×C151 | C2 | semidirect |
| 16. C2×Dic302 | C22 | semidirect |
| 20. C2×C22⋊D151 | C22 | semidirect |
| 23. C22×Dic151 | C22 | semidirect |
| 24. C2×C4×D151 | C22 | semidirect |
| 25. C4⋊Dic151 | C22 | semidirect |
| 26. C4⋊Dic151 | C22 | semidirect |
| 27. Dic151⋊C4 | C22 | semidirect |
| 28. Dic151⋊C4 | C22 | semidirect |
| 29. Dic151⋊C4 | C22 | semidirect |
| 30. Dic151⋊C4 | C22 | semidirect |
| 38. C22⋊Dic151 | C22 | semidirect |
| 39. C22⋊Dic151 | C22 | semidirect |
| 40. (C2×D151)⋊C4 | C22 | semidirect |
| 41. (C2×D151)⋊C4 | C22 | semidirect |
| 42. C4×Dic151 | C22 | semidirect |
| 43. C4×Dic151 | C22 | semidirect |
| 116. C151 | #538 | semidirect |
| 129. #120 | D151 | semidirect |