Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
433 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 433 conjugacy classes of subgroups — too many to draw. Only its 186 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 |
|---|---|---|
| 5. #69841 | C3 | direct (N × H) |
| 136. C32 | #1838 | semidirect |
| 161. C3 | #69841 | direct (N × H) |
| 162. C3 | C3×#1838 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#97 | 2 |
| C3×#4924 | 2 |
| C3×#4552 | 2 |
| C3×#1838 | 3 |
| #69841 | 3 |