Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
317 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 317 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 |
|---|---|---|
| 2. C2×C3×#216 | C2 | semidirect |
| 3. C2×C3×Dic12 | C2 | semidirect |
| 5. C32×#103 | C2 | semidirect |
| 7. C3×#810 | C2 | semidirect |
| 9. #4809 | C3 | direct (N × H) |
| 30. C2×#216 | C2×C3 | semidirect |
| 31. C2×Dic12 | C2×C3 | semidirect |
| 35. C3×#103 | D3 | semidirect |
| 36. C3×#103 | C2×C3 | semidirect |
| 39. #810 | C2×C3 | semidirect |
| 96. C2×C3×D3 | Q16 | semidirect |
| 109. #103 | C3×D3 | semidirect |
| 182. C2×D3 | C3×Q16 | semidirect |
| 201. C32 | #451 | semidirect |
| 244. C3 | #4809 | direct (N × H) |
| 245. C3 | C3×#451 | 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×#216 | 2 |
| C2×C3×Dic12 | 2 |
| C3×#897 | 2 |
| C32×#103 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×#810 | 2 |
| C3×#451 | 3 |
| #4809 | 3 |