Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
255 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 60 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×#509 | C2 | semidirect |
| 2. #10588876 | C2 | semidirect |
| 3. #10588873 | C2 | semidirect |
| 4. #10588831 | C2 | semidirect |
| 5. #10588240 | C2 | semidirect |
| 6. #10588193 | C2 | semidirect |
| 7. #10588188 | C2 | semidirect |
| 35. C9×Q16 | D4 | semidirect |
| 39. C9×D8 | D4 | semidirect |
| 87. #509 | D9 | semidirect |
| 166. Q16 | #611 | semidirect |
| 174. D8 | #611 | semidirect |
| 193. C9 | #2213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#509 | 2 |
| #10588876 | 2 |
| #10588873 | 2 |
| #10588831 | 2 |
| #10588240 | 2 |
| #10588193 | 2 |
| #10588188 | 2 |
| #71514 | 3 |