Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
321 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 321 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 4. C32×#103 | C2 | semidirect |
| 5. C3×#835 | C2 | semidirect |
| 6. C3×#816 | C2 | semidirect |
| 7. C3×#810 | C2 | semidirect |
| 9. #4802 | C3 | direct (N × H) |
| 12. C3×D3×Q8 | C4 | semidirect |
| 34. C3×#103 | D3 | semidirect |
| 35. C3×#103 | C2×C3 | semidirect |
| 36. #835 | C2×C3 | semidirect |
| 37. #816 | C2×C3 | semidirect |
| 38. #810 | C2×C3 | semidirect |
| 67. D3×Q8 | C3×C4 | semidirect |
| 105. #103 | C3×D3 | semidirect |
| 191. C32 | #419 | semidirect |
| 232. C3 | #4802 | direct (N × H) |
| 233. C3 | C3×#419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×Q8 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| C3×#892 | 2 |
| C32×#103 | 2 |
| C3×#835 | 2 |
| C3×#816 | 2 |
| C3×#810 | 2 |
| C3×#419 | 3 |
| #4802 | 3 |