Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
555 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 555 conjugacy classes of subgroups — too many to draw. Only its 136 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. #10589859 | C2 | semidirect |
| 2. C2×C9×D16 | C2 | semidirect |
| 3. #10588827 | C2 | semidirect |
| 4. #10588592 | C2 | semidirect |
| 5. #10588591 | C2 | semidirect |
| 6. D9×D16 | C2 | semidirect |
| 7. #10588584 | C2 | semidirect |
| 8. #10588581 | C2 | semidirect |
| 11. C2×C9×D8 | C22 | semidirect |
| 13. #63474 | C22 | semidirect |
| 15. D8×D9 | C22 | semidirect |
| 16. #63467 | C22 | semidirect |
| 18. C9×D16 | C22 | semidirect |
| 19. C9×D16 | C22 | semidirect |
| 20. C2×C9×C16 | C22 | semidirect |
| 21. #63386 | C22 | semidirect |
| 22. #63385 | C22 | semidirect |
| 23. #63371 | C22 | semidirect |
| 24. Dic72 | C22 | semidirect |
| 25. #63359 | C22 | semidirect |
| 26. D144 | C22 | semidirect |
| 27. #63357 | C22 | semidirect |
| 28. C16×D9 | C22 | semidirect |
| 104. C2×D16 | D9 | semidirect |
| 144. C2×D8 | C2×D9 | semidirect |
| 151. D16 | C2×D9 | semidirect |
| 152. D16 | C2×D9 | semidirect |
| 156. C2×C16 | C2×D9 | semidirect |
| 213. C9 | #3415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589859 | 2 |
| C2×C9×D16 | 2 |
| #10588827 | 2 |
| #10588592 | 2 |
| #10588591 | 2 |
| D9×D16 | 2 |
| #10588584 | 2 |
| #10588581 | 2 |
| #82019 | 3 |