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. C32×C4×M16 | C2 | semidirect |
| 4. #10592631 | C2 | semidirect |
| 5. #10589421 | C2 | semidirect |
| 13. C4×C4⋊(C3⋊D3) | C4 | semidirect |
| 16. C4×#634 | C4 | semidirect |
| 20. #63652 | C4 | semidirect |
| 22. C3×C4×M16 | D3 | semidirect |
| 37. C32×M16 | C2×C4 | semidirect |
| 49. C4×C3⋊Dic3 | C2×C4 | semidirect |
| 88. C4×M16 | C3⋊D3 | semidirect |
| 102. C3×M16 | C4×D3 | semidirect |
| 178. M16 | C4×C3⋊D3 | semidirect |
| 204. C32 | #1759 | semidirect |
| 243. C3 | #69866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3828 | 2 |
| C32×C4×M16 | 2 |
| C2×#63652 | 2 |
| #10592631 | 2 |
| #10589421 | 2 |
| #69866 | 3 |