Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
540 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 168 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. C9×#576 | C2 | semidirect |
| 2. #10589855 | C2 | semidirect |
| 3. #10588875 | C2 | semidirect |
| 4. #10588874 | C2 | semidirect |
| 5. C2×#63386 | C2 | semidirect |
| 6. #10588827 | C2 | semidirect |
| 7. #10588820 | C2 | semidirect |
| 16. #63467 | C22 | semidirect |
| 17. C2×Dic36 | C22 | semidirect |
| 18. #63388 | C22 | semidirect |
| 19. #63387 | C22 | semidirect |
| 20. #63386 | C22 | semidirect |
| 21. #63386 | C22 | semidirect |
| 22. #63385 | C22 | semidirect |
| 23. #63371 | C22 | semidirect |
| 24. C2×C9⋊C16 | C22 | semidirect |
| 88. #576 | D9 | semidirect |
| 189. C9 | #3416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#576 | 2 |
| #10589855 | 2 |
| #10588875 | 2 |
| #10588874 | 2 |
| C2×#63386 | 2 |
| #10588827 | 2 |
| #10588820 | 2 |
| #84008 | 3 |