Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1764 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 1764 conjugacy classes of subgroups — too many to draw. Only its 221 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×#413 | C2 | semidirect |
| 3. #10592939 | C2 | semidirect |
| 4. #10592838 | C2 | semidirect |
| 5. #10592830 | C2 | semidirect |
| 13. C2×#3828 | C4 | semidirect |
| 15. C22×C4⋊(C3⋊D3) | C4 | semidirect |
| 17. C2×C32×M16 | C22 | semidirect |
| 18. #64135 | C22 | semidirect |
| 25. C3×#413 | D3 | semidirect |
| 75. C2×C3×M16 | C2×D3 | semidirect |
| 118. #413 | C3⋊D3 | semidirect |
| 182. C2×M16 | C2×C3⋊D3 | semidirect |
| 280. C32 | #1795 | semidirect |
| 337. C3 | #70139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64366 | 2 |
| C32×#413 | 2 |
| #10592939 | 2 |
| #10592838 | 2 |
| #10592830 | 2 |
| #70139 | 3 |