Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
307 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 307 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 1. C32×#121 | C2 | semidirect |
| 2. C2×C3×#213 | C2 | semidirect |
| 3. C3×#930 | C2 | semidirect |
| 4. C2×C3×#208 | C2 | semidirect |
| 5. C3×#832 | C2 | semidirect |
| 6. C3×#809 | C2 | semidirect |
| 7. C3×#808 | C2 | semidirect |
| 9. #5039 | C3 | direct (N × H) |
| 27. C3×#121 | D3 | semidirect |
| 28. C3×#121 | C2×C3 | semidirect |
| 29. C2×#213 | C2×C3 | semidirect |
| 30. #930 | C2×C3 | semidirect |
| 31. C2×#208 | C2×C3 | semidirect |
| 35. #832 | C2×C3 | semidirect |
| 36. #809 | C2×C3 | semidirect |
| 37. #808 | C2×C3 | semidirect |
| 54. C3×C3⋊C8 | D4 | semidirect |
| 105. #121 | C3×D3 | semidirect |
| 152. C3⋊C8 | C3×D4 | semidirect |
| 213. C32 | #469 | semidirect |
| 264. C3 | #5039 | direct (N × H) |
| 265. C3 | C3×#469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#121 | 2 |
| C2×C3×#213 | 2 |
| C3×#930 | 2 |
| C2×C3×#208 | 2 |
| C3×#832 | 2 |
| C3×#809 | 2 |
| C3×#808 | 2 |
| C3×#469 | 3 |
| #5039 | 3 |