Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
273 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 76 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×#3711 | C2 | semidirect |
| 3. C2×#3710 | C2 | semidirect |
| 4. #63647 | C2 | semidirect |
| 5. C3×(C2×D3)⋊C8 | C2 | semidirect |
| 6. C3×#815 | C2 | semidirect |
| 7. Dic3⋊(C3⋊C8) | C2 | semidirect |
| 34. (C2×D3)⋊C8 | D3 | semidirect |
| 35. #815 | D3 | semidirect |
| 53. C3×C3⋊C8 | D4 | semidirect |
| 87. C2×C3⋊D3 | M16 | semidirect |
| 142. C3⋊C8 | D12 | semidirect |
| 194. C32 | #435 | semidirect |
| 239. C3 | #4706 | semidirect |
| 240. C3 | #4728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#626 | 2 |
| C2×#3711 | 2 |
| C2×#3710 | 2 |
| #63647 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×#815 | 2 |
| Dic3⋊(C3⋊C8) | 2 |
| #4728 | 3 |
| #4706 | 3 |