Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
322 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C2×C3×Dic24 | C2 | semidirect |
| 4. C3×#4517 | C2 | semidirect |
| 5. C3×#4506 | C2 | semidirect |
| 7. #71456 | C3 | direct (N × H) |
| 25. C2×Dic24 | C2×C3 | semidirect |
| 28. #4517 | C2×C3 | semidirect |
| 29. #4506 | C2×C3 | semidirect |
| 208. C32 | #2222 | semidirect |
| 237. C3 | #71456 | direct (N × H) |
| 238. C3 | C3×#2222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#504 | 2 |
| C3×#5143 | 2 |
| C2×C3×Dic24 | 2 |
| C3×#4517 | 2 |
| C3×#4506 | 2 |
| C3×#2222 | 3 |
| #71456 | 3 |