Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
241 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 241 conjugacy classes of subgroups — too many to draw. Only its 124 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. C2×C3×C3⋊C32 | C2 | semidirect |
| 4. #10589068 | C2 | direct (N × H) |
| 12. C3⋊(C3⋊C32) | C22 | semidirect |
| 13. C3×C3⋊C32 | C22 | semidirect |
| 21. C2×C3⋊C32 | D3 | semidirect |
| 47. C3⋊C32 | C2×D3 | semidirect |
| 111. C2×C32 | M64 | semidirect |
| 137. C32 | C2×M64 | semidirect |
| 149. C2×C3 | #4447 | semidirect |
| 150. C2×C3 | #4499 | semidirect |
| 161. C3 | C2×#4447 | semidirect |
| 162. C3 | C2×#4499 | semidirect |
| 164. C2 | #10589068 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×C16 | 2 |
| C2×C3⋊(C3⋊C32) | 2 |
| C2×C3×C3⋊C32 | 2 |
| #10589068 | 2 |
| C2×#4499 | 3 |
| C2×#4447 | 3 |