Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
501 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 501 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 3. #10588681 | C2 | semidirect |
| 4. #10588609 | C2 | semidirect |
| 6. C9×#339 | C2 | semidirect |
| 7. #10588234 | C2 | semidirect |
| 17. #63471 | C4 | semidirect |
| 53. C2×Dic18 | C2×C4 | semidirect |
| 56. C9×M16 | C2×C4 | semidirect |
| 135. #339 | D9 | semidirect |
| 276. M16 | C4×D9 | semidirect |
| 308. C9 | #1882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63471 | 2 |
| #10589625 | 2 |
| #10588681 | 2 |
| #10588609 | 2 |
| C2×#63364 | 2 |
| C9×#339 | 2 |
| #10588234 | 2 |
| #68775 | 3 |