Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
354 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 112 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. C22×C3⋊(C3⋊C8) | C2 | semidirect |
| 3. C3×#926 | C2 | semidirect |
| 4. #63565 | C2 | semidirect |
| 5. #63562 | C2 | semidirect |
| 11. C3×#235 | C4 | semidirect |
| 23. #926 | D3 | semidirect |
| 58. #235 | Dic3 | semidirect |
| 167. C32 | #416 | semidirect |
| 205. C3 | #5002 | semidirect |
| 206. C3 | #5233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#235 | 2 |
| C22×C3⋊(C3⋊C8) | 2 |
| C3×#926 | 2 |
| #63565 | 2 |
| #63562 | 2 |
| #5233 | 3 |
| #5002 | 3 |