Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
273 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 273 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 |
|---|---|---|
| 2. C2×C3×#214 | C2 | semidirect |
| 3. C2×C3×D3×C8 | C2 | semidirect |
| 4. C3×#897 | C2 | semidirect |
| 5. C32×#102 | C2 | semidirect |
| 6. C3×#816 | C2 | semidirect |
| 7. C3×#808 | C2 | semidirect |
| 9. #4778 | C3 | direct (N × H) |
| 28. C2×#214 | C2×C3 | semidirect |
| 29. C2×D3×C8 | C2×C3 | semidirect |
| 30. #897 | C2×C3 | semidirect |
| 34. C3×#102 | D3 | semidirect |
| 35. C3×#102 | C2×C3 | semidirect |
| 36. #816 | C2×C3 | semidirect |
| 37. #808 | C2×C3 | semidirect |
| 53. C3×C3⋊C8 | D4 | semidirect |
| 90. C2×C3×D3 | SD16 | semidirect |
| 103. #102 | C3×D3 | semidirect |
| 141. C3⋊C8 | C3×D4 | semidirect |
| 177. C2×D3 | C3×SD16 | semidirect |
| 193. C32 | #465 | semidirect |
| 238. C3 | #4778 | direct (N × H) |
| 239. C3 | C3×#465 | 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 |
| C2×C3×D3×C8 | 2 |
| C3×#897 | 2 |
| C32×#102 | 2 |
| C3×#816 | 2 |
| C3×#808 | 2 |
| C3×#465 | 3 |
| #4778 | 3 |