Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
351 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 351 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. #10588216 | C2 | semidirect |
| 7. C22×Q8×C9 | C4 | semidirect |
| 10. C9×#123 | C4 | semidirect |
| 14. C9×#117 | C4 | semidirect |
| 140. C22×Q8 | Dic9 | semidirect |
| 144. #123 | Dic9 | semidirect |
| 149. #117 | Dic9 | semidirect |
| 226. C9 | #2123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#536 | 2 |
| #10588920 | 2 |
| #10588915 | 2 |
| #10588216 | 2 |
| #71870 | 3 |