Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
504 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. C32×#334 | C2 | semidirect |
| 4. #10589345 | C2 | semidirect |
| 5. #10589323 | C2 | semidirect |
| 20. C3×#334 | D3 | semidirect |
| 71. #334 | C3⋊D3 | semidirect |
| 156. C32 | #1568 | semidirect |
| 189. C3 | #68530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592534 | 2 |
| C4×C8×C3⋊D3 | 2 |
| C32×#334 | 2 |
| #10589345 | 2 |
| #10589323 | 2 |
| #68530 | 3 |