Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
456 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 4. C2×#63382 | C2 | semidirect |
| 5. #10588804 | C2 | semidirect |
| 6. C9×#338 | C2 | semidirect |
| 7. #10588236 | C2 | semidirect |
| 20. C2×#3664 | C4 | semidirect |
| 22. C2×Dic36 | C4 | semidirect |
| 121. #338 | D9 | semidirect |
| 269. C9 | #1902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63471 | 2 |
| #10589847 | 2 |
| #10588819 | 2 |
| C2×#63382 | 2 |
| #10588804 | 2 |
| C9×#338 | 2 |
| #10588236 | 2 |
| #68725 | 3 |