Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
274 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 274 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. C2×C32×SD16 | C2 | semidirect |
| 2. C3×#946 | C2 | semidirect |
| 4. C2×C3×ΓL(1,𝔽25) | C2 | semidirect |
| 5. C3×#835 | C2 | semidirect |
| 6. C3×#832 | C2 | semidirect |
| 7. C3×#818 | C2 | semidirect |
| 9. #5174 | C3 | direct (N × H) |
| 24. C2×C3×SD16 | D3 | semidirect |
| 25. C2×C3×SD16 | C2×C3 | semidirect |
| 29. #946 | C2×C3 | semidirect |
| 31. C2×ΓL(1,𝔽25) | C2×C3 | semidirect |
| 35. #835 | C2×C3 | semidirect |
| 36. #832 | C2×C3 | semidirect |
| 37. #818 | C2×C3 | semidirect |
| 52. C32×C8 | D4 | semidirect |
| 98. C2×SD16 | C3×D3 | semidirect |
| 142. C3×C8 | #67 | semidirect |
| 143. C3×C8 | C3×D4 | semidirect |
| 196. C32 | #468 | semidirect |
| 212. C8 | C3×#67 | semidirect |
| 241. C3 | #5174 | direct (N × H) |
| 242. C3 | C3×#468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×SD16 | 2 |
| C3×#946 | 2 |
| C3×#938 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| C3×#835 | 2 |
| C3×#832 | 2 |
| C3×#818 | 2 |
| C3×#468 | 3 |
| #5174 | 3 |