Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
504 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 145 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. C32×#364 | C2 | semidirect |
| 4. #10589377 | C2 | semidirect |
| 5. #10589329 | C2 | semidirect |
| 20. C3×#364 | D3 | semidirect |
| 72. #364 | C3⋊D3 | direct (N × H) |
| 130. C3⋊D3 | #364 | direct (N × H) |
| 158. C32 | C2×#364 | semidirect |
| 189. C3 | D3×#364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×M32 | 2 |
| C4×C8×C3⋊D3 | 2 |
| C32×#364 | 2 |
| #10589377 | 2 |
| #10589329 | 2 |
| D3×#364 | 3 |