Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
417 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 417 conjugacy classes of subgroups — too many to draw. Only its 108 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×#4463 | C2 | semidirect |
| 4. #10589135 | C2 | semidirect |
| 21. #4463 | D3 | semidirect |
| 164. C3⋊D3 | #364 | semidirect |
| 201. C32 | C2×#364 | semidirect |
| 237. C3 | D3×#364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C8×C3⋊D3 | 2 |
| #10590625 | 2 |
| C3×#4463 | 2 |
| #10589135 | 2 |
| D3×#364 | 3 |