Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
480 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 150 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. C4×C9×M16 | C2 | semidirect |
| 4. #10588612 | C2 | semidirect |
| 5. #10588235 | C2 | semidirect |
| 13. C4×D36 | C4 | semidirect |
| 16. C4×Dic18 | C4 | semidirect |
| 20. #63384 | C4 | semidirect |
| 37. C9×M16 | C2×C4 | semidirect |
| 49. C4×Dic9 | C2×C4 | semidirect |
| 88. C4×M16 | D9 | semidirect |
| 178. M16 | C4×D9 | semidirect |
| 204. C9 | #1759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3697 | 2 |
| C4×C9×M16 | 2 |
| C2×#63384 | 2 |
| #10588612 | 2 |
| #10588235 | 2 |
| #69866 | 3 |