Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
756 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 169 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×#432 | C2 | semidirect |
| 3. #10592636 | C2 | semidirect |
| 4. #10589336 | C2 | semidirect |
| 11. #64083 | C4 | semidirect |
| 13. C4×C4⋊(C3⋊D3) | C4 | semidirect |
| 14. #64078 | C4 | semidirect |
| 22. C3×#432 | D3 | semidirect |
| 84. #432 | C3⋊D3 | semidirect |
| 199. C32 | #1514 | semidirect |
| 242. C3 | #70835 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595948 | 2 |
| C32×#432 | 2 |
| #10592636 | 2 |
| #10589336 | 2 |
| #70835 | 3 |