Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
259 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 259 conjugacy classes of subgroups — too many to draw. Only its 90 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. C3×#869 | C2 | semidirect |
| 4. C32×C4⋊C8 | C2 | semidirect |
| 5. C3×#816 | C2 | semidirect |
| 7. #4841 | C3 | direct (N × H) |
| 23. #869 | C2×C3 | semidirect |
| 25. C3×C4⋊C8 | D3 | semidirect |
| 26. C3×C4⋊C8 | C2×C3 | semidirect |
| 28. #816 | C2×C3 | semidirect |
| 69. C32×C4 | SD16 | semidirect |
| 77. C4⋊C8 | C3×D3 | semidirect |
| 138. C3×C4 | #204 | semidirect |
| 139. C3×C4 | C3×SD16 | semidirect |
| 146. C32 | #461 | semidirect |
| 177. C4 | C3×#204 | semidirect |
| 181. C3 | #4841 | direct (N × H) |
| 182. C3 | C3×#461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#204 | 2 |
| C3×C4×D12 | 2 |
| C3×#869 | 2 |
| C32×C4⋊C8 | 2 |
| C3×#816 | 2 |
| C3×#461 | 3 |
| #4841 | 3 |