Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
8694 conjugacy classes of subgroups; only the 3576 normal subgroups are shown.
This group has 8694 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 | 2−1+6 |
| 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. D9×2−1+4 | C2 | semidirect |
| 3. #10593141 | C2 | semidirect |
| 4. #10593139 | C2 | semidirect |
| 5. C2×#63716 | 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. #63716 | C22 | semidirect |
| 12. #63715 | C22 | semidirect |
| 13. #41×D9 | C22 | semidirect |
| 14. #63713 | C22 | semidirect |
| 15. C2×Q8×D9 | C22 | semidirect |
| 16. #63710 | C22 | semidirect |
| 17. C2×#3699 | C22 | semidirect |
| 18. C2×#3697 | C22 | semidirect |
| 19. C22×Dic18 | C22 | semidirect |
| 71. #585 | D9 | semidirect |
| 101. 2−1+4 | C2×D9 | semidirect |
| 104. H(5,𝔽2) | C2×D9 | semidirect |
| 108. C2×#41 | C2×D9 | semidirect |
| 151. C9 | 2−1+6 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#585 | 2 |
| D9×2−1+4 | 2 |
| #10593141 | 2 |
| #10593139 | 2 |
| C2×#63716 | 2 |
| #87572 | 3 |