Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
161 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 161 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
| 3. C3×#4506 | C2 | semidirect |
| 16. #4506 | D3 | semidirect |
| 130. C32 | #1417 | semidirect |
| 153. C3 | #67585 | semidirect |
| 154. C3 | #67829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4904 | 2 |
| C2×C3⋊(C3⋊C32) | 2 |
| C3×#4506 | 2 |
| #67829 | 3 |
| #67585 | 3 |