Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
213 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 213 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 |
|---|---|---|
| 2. C2×C3×C3⋊C32 | C2 | semidirect |
| 4. #67803 | C3 | direct (N × H) |
| 14. C2×C3⋊C32 | C2×C3 | semidirect |
| 70. C22×C32 | C32 | semidirect |
| 123. C22×C3 | C3⋊C32 | semidirect |
| 124. C22×C3 | C3×C32 | semidirect |
| 136. C32 | C22⋊C32 | semidirect |
| 159. C22 | C3×C3⋊C32 | semidirect |
| 165. C3 | #67803 | direct (N × H) |
| 166. C3 | C3×C22⋊C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C16 | 2 |
| C2×C3×C3⋊C32 | 2 |
| C3×C22⋊C32 | 3 |
| #67803 | 3 |