Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
732 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10589830 | C2 | semidirect |
| 3. C9×#492 | C2 | semidirect |
| 4. #10588849 | C2 | semidirect |
| 5. #10588843 | C2 | semidirect |
| 6. #10588770 | C2 | semidirect |
| 7. #10588750 | C2 | semidirect |
| 8. #10588376 | C2 | semidirect |
| 9. #10588367 | C2 | semidirect |
| 14. C2×C9×SD16 | C22 | semidirect |
| 15. C9×C4⋊Q8 | C22 | semidirect |
| 18. Q8×Dic9 | C22 | semidirect |
| 19. C2×#3675 | C22 | semidirect |
| 29. #63431 | C22 | semidirect |
| 30. C4×C8×C9 | C22 | semidirect |
| 31. #63392 | C22 | semidirect |
| 32. #63380 | C22 | semidirect |
| 34. Dic9⋊C8 | C22 | semidirect |
| 35. C4×C9⋊C8 | C22 | semidirect |
| 131. C4×D9 | SD16 | semidirect |
| 138. #492 | D9 | semidirect |
| 201. C2×SD16 | C2×D9 | semidirect |
| 203. C4⋊Q8 | C2×D9 | semidirect |
| 221. C4×C8 | C2×D9 | semidirect |
| 311. C9 | #3208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589830 | 2 |
| D9×#127 | 2 |
| C9×#492 | 2 |
| #10588849 | 2 |
| #10588843 | 2 |
| #10588770 | 2 |
| #10588750 | 2 |
| #10588376 | 2 |
| #10588367 | 2 |
| #81766 | 3 |