Finite Group DatabasebetaFinite Group DatabasebetaOrder 9664.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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 | #525 |
| 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. C2×#14559005 | C2 | semidirect |
| 2. C22×C4×D151 | C2 | semidirect |
| 3. #18012724 | C2 | semidirect |
| 4. #18012715 | C2 | semidirect |
| 5. #18012714 | C2 | semidirect |
| 6. #18012713 | C2 | semidirect |
| 7. #18012709 | C2 | semidirect |
| 8. #18012701 | C2 | semidirect |
| 9. (C22⋊D151)⋊C4 | C2 | semidirect |
| 10. #18012697 | C2 | semidirect |
| 11. C22⋊Q8×C151 | C2 | semidirect |
| 16. C2×D604 | C22 | semidirect |
| 24. C2×C4×D151 | C22 | semidirect |
| 25. C4⋊Dic151 | C22 | semidirect |
| 26. Dic151⋊C4 | C22 | semidirect |
| 29. (C2×D151)⋊C4 | C22 | semidirect |
| 30. (C2×D151)⋊C4 | C22 | semidirect |
| 31. C4×Dic151 | C22 | semidirect |
| 32. C2×Q8×C151 | C22 | semidirect |
| 34. C4⋊C4×C151 | C22 | semidirect |
| 35. C4⋊C4×C151 | C22 | semidirect |
| 55. C4×D151 | D4 | semidirect |
| 65. C22×C151 | #41 | semidirect |
| 76. C2×D151 | #41 | semidirect |
| 91. C151 | #525 | semidirect |
| 97. C22⋊Q8 | D151 | semidirect |
| 106. C2×Q8 | C2×D151 | semidirect |
| 121. C4⋊C4 | C2×D151 | semidirect |
| 122. C4⋊C4 | C2×D151 | semidirect |
| 167. C22 | #14559005 | semidirect |