Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
186 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 56 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. C2×C3×C3⋊C32 | C2 | semidirect |
| 18. #4506 | D3 | semidirect |
| 19. C2×C3⋊C32 | D3 | semidirect |
| 143. C32 | #1417 | semidirect |
| 167. C3 | #67585 | semidirect |
| 168. C3 | #67598 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592603 | 2 |
| C3×#4506 | 2 |
| C2×C3×C3⋊C32 | 2 |
| #67598 | 3 |
| #67585 | 3 |