Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
265 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 265 conjugacy classes of subgroups — too many to draw. Only its 64 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. C2×C3×#214 | C2 | semidirect |
| 3. #63856 | C2 | semidirect |
| 4. C2×#3711 | C2 | semidirect |
| 5. #63659 | C2 | semidirect |
| 6. #63575 | C2 | semidirect |
| 7. #63565 | C2 | semidirect |
| 27. C2×#214 | D3 | semidirect |
| 53. C3×C3⋊C8 | D4 | semidirect |
| 141. C3⋊C8 | #67 | semidirect |
| 193. C32 | #468 | semidirect |
| 238. C3 | #5042 | semidirect |
| 239. C3 | #5174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#938 | 2 |
| C2×C3×#214 | 2 |
| #63856 | 2 |
| C2×#3711 | 2 |
| #63659 | 2 |
| #63575 | 2 |
| #63565 | 2 |
| #5174 | 3 |
| #5042 | 3 |