Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
219 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 219 conjugacy classes of subgroups — too many to draw. Only its 76 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×#443 | C2 | semidirect |
| 3. #10588380 | C2 | semidirect |
| 4. #10588244 | C2 | semidirect |
| 5. #10588173 | C2 | semidirect |
| 6. #10588170 | C2 | semidirect |
| 7. C4×C9⋊C16 | C2 | semidirect |
| 16. #63388 | C4 | semidirect |
| 17. #63387 | C4 | semidirect |
| 18. #63386 | C4 | semidirect |
| 19. #63385 | C4 | semidirect |
| 85. #443 | D9 | semidirect |
| 181. C9 | #2178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#443 | 2 |
| #10588874 | 2 |
| #10588380 | 2 |
| #10588244 | 2 |
| #10588173 | 2 |
| #10588170 | 2 |
| C4×C9⋊C16 | 2 |
| #70921 | 3 |