Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
756 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 209 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. #10592636 | C2 | semidirect |
| 3. #10592625 | C2 | semidirect |
| 4. #10589403 | C2 | semidirect |
| 7. C32×C4⋊Q8 | C4 | semidirect |
| 8. C32×#127 | C4 | semidirect |
| 13. C32×C4×D4 | C4 | semidirect |
| 47. C3×C4⋊Q8 | Dic3 | semidirect |
| 48. C3×#127 | Dic3 | semidirect |
| 53. C3×C4×D4 | Dic3 | semidirect |
| 123. C4⋊Q8 | C3⋊Dic3 | semidirect |
| 124. #127 | C3⋊Dic3 | semidirect |
| 129. C4×D4 | C3⋊Dic3 | semidirect |
| 199. C32 | #1514 | semidirect |
| 242. C3 | #71813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#532 | 2 |
| #10592636 | 2 |
| #10592625 | 2 |
| #10589403 | 2 |
| #71813 | 3 |