Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
293 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 293 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 4. #67820 | C3 | direct (N × H) |
| 144. C32 | #1385 | semidirect |
| 170. C3 | #67820 | direct (N × H) |
| 171. C3 | C3×#1385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M32 | 2 |
| C2×C3×#819 | 2 |
| C3×#1385 | 3 |
| #67820 | 3 |