Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
801 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 801 conjugacy classes of subgroups — too many to draw. Only its 192 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 |
|---|---|---|
| 3. C3×#4683 | C2 | semidirect |
| 4. #10590875 | C2 | semidirect |
| 5. #10590874 | C2 | semidirect |
| 8. #10590314 | C2 | semidirect |
| 35. #4683 | D3 | semidirect |
| 185. C3⋊D3 | #499 | semidirect |
| 220. C32 | C2×#499 | semidirect |
| 251. C3 | D3×#499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593948 | 2 |
| C4×C8×C3⋊D3 | 2 |
| C3×#4683 | 2 |
| #10590875 | 2 |
| #10590874 | 2 |
| #10590687 | 2 |
| #10590685 | 2 |
| #10590314 | 2 |
| D3×#499 | 3 |