Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
792 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 155 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. C32×#416 | C2 | semidirect |
| 3. #10592939 | C2 | semidirect |
| 4. #10592812 | C2 | semidirect |
| 5. #10592801 | C2 | semidirect |
| 6. #10592705 | C2 | semidirect |
| 7. #10589397 | C2 | semidirect |
| 29. C3×#416 | D3 | semidirect |
| 126. #416 | C3⋊D3 | semidirect |
| 293. C32 | #2053 | semidirect |
| 349. C3 | #70296 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596293 | 2 |
| C32×#416 | 2 |
| #10592939 | 2 |
| #10592812 | 2 |
| #10592801 | 2 |
| #10592705 | 2 |
| #10589397 | 2 |
| #70296 | 3 |