Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
774 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 310 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. #10588660 | C2 | semidirect |
| 3. C4⋊C4×Dic9 | C2 | semidirect |
| 6. #10588617 | C2 | semidirect |
| 7. C42×Dic9 | C2 | semidirect |
| 10. C9×#126 | C4 | semidirect |
| 38. C9×C4⋊C4 | C2×C4 | semidirect |
| 40. C42×C9 | C2×C4 | semidirect |
| 114. Dic9 | #126 | direct (N × H) |
| 116. #126 | Dic9 | direct (N × H) |
| 161. C4⋊C4 | C2×Dic9 | semidirect |
| 167. C42 | C2×Dic9 | semidirect |
| 180. C9 | C4×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#126 | 2 |
| #10588660 | 2 |
| C4⋊C4×Dic9 | 2 |
| #10588631 | 2 |
| C22⋊C4×Dic9 | 2 |
| #10588617 | 2 |
| C42×Dic9 | 2 |
| Dic3×#126 | 3 |