Finite Group DatabasebetaFinite Group DatabasebetaOrder 9664.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 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 | #120×C151 | C2 |
| hypercenter | #120 | D151 |
| hypocenter | C151 | #560 |
| 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. #18012735 | C2 | semidirect |
| 2. #18012732 | C2 | semidirect |
| 3. #18012721 | C2 | semidirect |
| 4. #18012720 | C2 | semidirect |
| 5. #18012712 | C2 | semidirect |
| 6. #18012711 | C2 | semidirect |
| 7. #18012710 | C2 | semidirect |
| 8. #18012708 | C2 | semidirect |
| 9. #120×C151 | C2 | semidirect |
| 10. C2×D604 | C22 | semidirect |
| 14. C2×C22⋊D151 | C22 | semidirect |
| 15. C22×Dic151 | C22 | semidirect |
| 16. C2×C4×D151 | C22 | semidirect |
| 17. C4⋊Dic151 | C22 | semidirect |
| 18. Dic151⋊C4 | C22 | semidirect |
| 19. Dic151⋊C4 | C22 | semidirect |
| 23. C22⋊Dic151 | C22 | semidirect |
| 24. (C2×D151)⋊C4 | C22 | semidirect |
| 25. C4×Dic151 | C22 | semidirect |
| 74. C151 | #560 | semidirect |
| 84. #120 | D151 | semidirect |