Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
600 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 146 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. #10589790 | C2 | semidirect |
| 3. C9×#488 | C2 | semidirect |
| 4. #10588749 | C2 | semidirect |
| 5. #10588735 | C2 | semidirect |
| 6. #10588484 | C2 | semidirect |
| 7. #10588472 | C2 | semidirect |
| 8. #10588452 | C2 | semidirect |
| 9. #10588440 | C2 | semidirect |
| 10. #10588379 | C2 | semidirect |
| 11. C4×C8×D9 | C2 | semidirect |
| 139. #488 | D9 | semidirect |
| 292. C9 | #3131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589790 | 2 |
| #10589770 | 2 |
| C9×#488 | 2 |
| #10588749 | 2 |
| #10588735 | 2 |
| #10588484 | 2 |
| #10588472 | 2 |
| #10588452 | 2 |
| #10588440 | 2 |
| #10588379 | 2 |
| C4×C8×D9 | 2 |
| #81637 | 3 |