Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
8988 conjugacy classes of subgroups; only the 3576 normal subgroups are shown.
This group has 8988 conjugacy classes of subgroups — too many to draw. Only its 3576 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C25×D9 |
| commutator, cosocle | C2×C9 | C26 |
| Frattini, socle | C2×C3 | C25×D3 |
| Fitting | C9×#585 | C2 |
| hypercenter | #585 | D9 |
| hypocenter | C9 | H(7,𝔽2) |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×#585 | C2 | semidirect |
| 2. #10593143 | C2 | semidirect |
| 3. D9×H(5,𝔽2) | C2 | semidirect |
| 4. #10593139 | C2 | semidirect |
| 5. C2×#63715 | C2 | semidirect |
| 7. C9×2−1+4 | C22 | semidirect |
| 8. C9×H(5,𝔽2) | C22 | semidirect |
| 9. C2×C9×#41 | C22 | semidirect |
| 10. #63716 | C22 | semidirect |
| 11. #63715 | C22 | semidirect |
| 12. #63715 | C22 | semidirect |
| 13. #41×D9 | C22 | semidirect |
| 14. #63713 | C22 | semidirect |
| 15. C2×#3701 | C22 | semidirect |
| 16. #63710 | C22 | semidirect |
| 17. C2×D4×D9 | C22 | semidirect |
| 18. C2×#3697 | C22 | semidirect |
| 19. C22×D36 | C22 | semidirect |
| 25. C23×D9 | C23 | semidirect |
| 26. C9×#41 | C23 | semidirect |
| 27. C9×#41 | C23 | semidirect |
| 28. C2×Q8×C9 | C23 | semidirect |
| 29. C2×D4×C9 | C23 | semidirect |
| 30. C22×C4×C9 | C23 | semidirect |
| 31. C2×#611 | C23 | semidirect |
| 32. #3701 | C23 | semidirect |
| 33. Q8×D9 | C23 | semidirect |
| 34. #3699 | C23 | semidirect |
| 35. D4×D9 | C23 | semidirect |
| 36. #3697 | C23 | semidirect |
| 37. #3697 | C23 | semidirect |
| 38. C2×D36 | C23 | semidirect |
| 39. C2×D36 | C23 | semidirect |
| 40. C2×C4×D9 | C23 | semidirect |
| 41. C2×Dic18 | C23 | semidirect |
| 72. #585 | D9 | semidirect |
| 101. 2−1+4 | C2×D9 | semidirect |
| 105. H(5,𝔽2) | C2×D9 | semidirect |
| 109. C2×#41 | C2×D9 | semidirect |
| 134. #41 | C22×D9 | semidirect |
| 135. #41 | C22×D9 | semidirect |
| 138. C2×Q8 | C22×D9 | semidirect |
| 143. C2×D4 | C22×D9 | semidirect |
| 145. C22×C4 | C22×D9 | semidirect |
| 153. C9 | H(7,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#585 | 2 |
| #10593143 | 2 |
| D9×H(5,𝔽2) | 2 |
| #10593139 | 2 |
| C2×#63715 | 2 |
| #87574 | 3 |