Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1032 conjugacy classes of subgroups; only the 294 normal subgroups are shown.
This group has 1032 conjugacy classes of subgroups — too many to draw. Only its 294 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. #10588927 | C2 | semidirect |
| 3. #10588901 | C2 | semidirect |
| 4. #10588900 | C2 | semidirect |
| 5. #10588631 | C2 | semidirect |
| 9. C23×Dic9 | C22 | semidirect |
| 10. C9×#120 | C4 | semidirect |
| 14. C2×#3676 | C22 | semidirect |
| 15. C2×C4⋊Dic9 | C22 | semidirect |
| 16. C2×C4×Dic9 | C22 | semidirect |
| 17. C9⋊#95 | C22 | semidirect |
| 25. C24×C9 | C2×C4 | semidirect |
| 35. C9×C22⋊C4 | C2×C4 | semidirect |
| 115. #120 | Dic9 | semidirect |
| 151. C24 | C2×Dic9 | semidirect |
| 165. C22⋊C4 | C2×Dic9 | semidirect |
| 182. C9 | #2375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#120 | 2 |
| #10588927 | 2 |
| #10588901 | 2 |
| #10588900 | 2 |
| #10588631 | 2 |
| #82580 | 3 |