Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
205 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 205 conjugacy classes of subgroups — too many to draw. Only its 66 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. C3×#4506 | C2 | semidirect |
| 3. C3×#4499 | C2 | semidirect |
| 5. #67825 | C3 | direct (N × H) |
| 17. #4506 | C2×C3 | semidirect |
| 18. #4499 | C2×C3 | semidirect |
| 129. C32 | #1419 | semidirect |
| 152. C3 | #67825 | direct (N × H) |
| 153. C3 | C3×#1419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D16 | 2 |
| C3×#4506 | 2 |
| C3×#4499 | 2 |
| C3×#1419 | 3 |
| #67825 | 3 |