Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
273 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 76 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. C2×C3×Dic24 | C2 | semidirect |
| 3. C2×C3×C3⋊C32 | C2 | semidirect |
| 4. #10589074 | C2 | direct (N × H) |
| 13. C3×Dic24 | C22 | semidirect |
| 14. C3×C3⋊C32 | C22 | semidirect |
| 16. C2×Dic24 | D3 | semidirect |
| 22. C2×C3⋊C32 | D3 | semidirect |
| 45. Dic24 | C2×D3 | semidirect |
| 53. C3⋊C32 | C2×D3 | semidirect |
| 129. C2×C32 | SD64 | semidirect |
| 158. C32 | C2×SD64 | semidirect |
| 170. C2×C3 | #4449 | semidirect |
| 171. C2×C3 | #4521 | semidirect |
| 184. C3 | C2×#4449 | semidirect |
| 185. C3 | C2×#4521 | semidirect |
| 187. C2 | #10589074 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63626 | 2 |
| C2×C3×Dic24 | 2 |
| C2×C3×C3⋊C32 | 2 |
| #10589074 | 2 |
| C2×#4521 | 3 |
| C2×#4449 | 3 |