Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
226 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 78 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×#107 | C2 | semidirect |
| 5. C3×#816 | C2 | semidirect |
| 6. C3×#810 | C2 | semidirect |
| 7. C3×#807 | C2 | semidirect |
| 9. #4884 | C3 | direct (N × H) |
| 27. C3×#107 | D3 | semidirect |
| 28. C3×#107 | C2×C3 | semidirect |
| 33. #816 | C2×C3 | semidirect |
| 34. #810 | C2×C3 | semidirect |
| 35. #807 | C2×C3 | semidirect |
| 90. #107 | C3×D3 | semidirect |
| 168. C32 | #484 | semidirect |
| 206. C3 | #4884 | direct (N × H) |
| 207. C3 | C3×#484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#897 | 2 |
| C3×D3×C4⋊C4 | 2 |
| C32×#107 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×#816 | 2 |
| C3×#810 | 2 |
| C3×#807 | 2 |
| C3×#484 | 3 |
| #4884 | 3 |