Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
326 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×C32×D8 | C2 | semidirect |
| 2. C3×#940 | C2 | semidirect |
| 3. C3×#936 | C2 | semidirect |
| 4. C2×C3×#214 | C2 | semidirect |
| 5. C2×C3×#213 | C2 | semidirect |
| 6. C2×C3×#204 | C2 | semidirect |
| 7. C3×#815 | C2 | semidirect |
| 9. #5154 | C3 | direct (N × H) |
| 27. C2×C3×D8 | D3 | semidirect |
| 28. C2×C3×D8 | C2×C3 | semidirect |
| 31. #940 | C2×C3 | semidirect |
| 32. #936 | C2×C3 | semidirect |
| 33. C2×#214 | C2×C3 | semidirect |
| 34. C2×#213 | C2×C3 | semidirect |
| 35. C2×#204 | C2×C3 | semidirect |
| 37. #815 | C2×C3 | semidirect |
| 53. C32×C8 | D4 | semidirect |
| 54. C3×C3⋊C8 | D4 | semidirect |
| 100. C2×D8 | C3×D3 | semidirect |
| 143. C3×C8 | #67 | semidirect |
| 144. C3×C8 | C3×D4 | semidirect |
| 145. C3⋊C8 | C3×D4 | semidirect |
| 193. C32 | #496 | semidirect |
| 210. C8 | C3×#67 | semidirect |
| 237. C3 | #5154 | direct (N × H) |
| 238. C3 | C3×#496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D8 | 2 |
| C3×#940 | 2 |
| C3×#936 | 2 |
| C2×C3×#214 | 2 |
| C2×C3×#213 | 2 |
| C2×C3×#204 | 2 |
| C3×#815 | 2 |
| C3×#496 | 3 |
| #5154 | 3 |