Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 124 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×#568 | C2 | semidirect |
| 3. #10588920 | C2 | semidirect |
| 4. #10588819 | C2 | semidirect |
| 5. #10588235 | C2 | semidirect |
| 12. #63509 | C4 | semidirect |
| 13. #63506 | C4 | semidirect |
| 14. #63502 | C4 | semidirect |
| 16. #63498 | C4 | semidirect |
| 44. C9×M16 | D4 | semidirect |
| 97. #568 | D9 | semidirect |
| 208. M16 | #611 | semidirect |
| 235. C9 | #1884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#568 | 2 |
| #10589934 | 2 |
| #10588920 | 2 |
| #10588819 | 2 |
| #10588235 | 2 |
| #72021 | 3 |