Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
600 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 186 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 |
|---|---|---|
| 2. #10589572 | C2 | semidirect |
| 3. #10588917 | C2 | semidirect |
| 4. #10588759 | C2 | semidirect |
| 5. #10588750 | C2 | semidirect |
| 6. #10588735 | C2 | semidirect |
| 7. C2×C4×C9⋊C8 | C2 | semidirect |
| 198. C9 | #3131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#532 | 2 |
| #10589572 | 2 |
| #10588917 | 2 |
| #10588759 | 2 |
| #10588750 | 2 |
| #10588735 | 2 |
| C2×C4×C9⋊C8 | 2 |
| #83281 | 3 |