Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
325 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 325 conjugacy classes of subgroups — too many to draw. Only its 72 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×#216 | C2 | semidirect |
| 3. #63856 | C2 | semidirect |
| 4. C2×#3715 | C2 | semidirect |
| 5. #63662 | C2 | semidirect |
| 6. #63563 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊C8) | C2 | semidirect |
| 29. C2×#216 | D3 | semidirect |
| 208. C32 | #452 | semidirect |
| 255. C3 | #5187 | semidirect |
| 256. C3 | #5239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#239 | 2 |
| C2×C3×#216 | 2 |
| #63856 | 2 |
| C2×#3715 | 2 |
| #63662 | 2 |
| #63563 | 2 |
| (C2×D3)⋊(C3⋊C8) | 2 |
| #5239 | 3 |
| #5187 | 3 |