Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
960 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 261 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×#63664 | C2 | semidirect |
| 3. #10592631 | C2 | semidirect |
| 4. #10592623 | C2 | semidirect |
| 7. C32×C4⋊Q8 | C4 | semidirect |
| 8. C32×#127 | C4 | semidirect |
| 9. C32×#124 | C4 | semidirect |
| 38. C4×C3⋊Dic3 | D4 | semidirect |
| 43. C3×C4⋊Q8 | Dic3 | semidirect |
| 44. C3×#127 | Dic3 | semidirect |
| 45. C3×#124 | Dic3 | semidirect |
| 110. C4⋊Q8 | C3⋊Dic3 | semidirect |
| 111. #127 | C3⋊Dic3 | semidirect |
| 112. #124 | C3⋊Dic3 | semidirect |
| 174. C32 | #1963 | semidirect |
| 210. C3 | #71816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#532 | 2 |
| C2×#63664 | 2 |
| #10592631 | 2 |
| #10592623 | 2 |
| #71816 | 3 |