Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
219 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 219 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 3. C32×#108 | C2 | semidirect |
| 4. C3×#822 | C2 | semidirect |
| 5. C3×#819 | C2 | semidirect |
| 7. #4893 | C3 | direct (N × H) |
| 23. C3×#108 | D3 | semidirect |
| 24. C3×#108 | C2×C3 | semidirect |
| 25. #822 | C2×C3 | semidirect |
| 26. #819 | C2×C3 | semidirect |
| 65. #108 | C3×D3 | semidirect |
| 113. C32 | #430 | semidirect |
| 138. C3 | #4893 | direct (N × H) |
| 139. C3 | C3×#430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D3×M16 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| C32×#108 | 2 |
| C3×#822 | 2 |
| C3×#819 | 2 |
| C3×#430 | 3 |
| #4893 | 3 |