Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
912 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 4. C2×#63651 | C2 | semidirect |
| 5. #10592819 | C2 | semidirect |
| 6. C32×#338 | C2 | semidirect |
| 7. #10589422 | C2 | semidirect |
| 20. C2×#3746 | C4 | semidirect |
| 21. C2×#3744 | C4 | semidirect |
| 31. C3×#338 | D3 | semidirect |
| 121. #338 | C3⋊D3 | semidirect |
| 269. C32 | #1902 | semidirect |
| 317. C3 | #68725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64118 | 2 |
| #10596216 | 2 |
| #10592838 | 2 |
| C2×#63651 | 2 |
| #10592819 | 2 |
| C32×#338 | 2 |
| #10589422 | 2 |
| #68725 | 3 |