Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
306 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 88 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. C3×#3746 | C2 | semidirect |
| 3. C32×Dic12 | C2 | semidirect |
| 5. C3×#3719 | C2 | semidirect |
| 8. D3×Dic12 | C3 | direct (N × H) |
| 21. #3746 | C2×C3 | semidirect |
| 28. C3×Dic12 | D3 | direct (N × H) |
| 29. C3×Dic12 | C2×C3 | semidirect |
| 33. #3719 | C2×C3 | semidirect |
| 72. C32×D3 | Q16 | semidirect |
| 89. Dic12 | C3×D3 | direct (N × H) |
| 115. C33 | C2×Q16 | semidirect |
| 154. C3×D3 | Dic12 | direct (N × H) |
| 155. C3×D3 | C3×Q16 | semidirect |
| 188. C32 | C2×Dic12 | semidirect |
| 189. C32 | D3×Q16 | semidirect |
| 190. C32 | C2×C3×Q16 | semidirect |
| 208. D3 | C3×Dic12 | direct (N × H) |
| 218. C3 | D3×Dic12 | direct (N × H) |
| 219. C3 | C2×C3×Dic12 | semidirect |
| 220. C3 | C3×D3×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D3×Dic6 | 2 |
| C3×#3746 | 2 |
| C32×Dic12 | 2 |
| C32×D3×C8 | 2 |
| C3×#3719 | 2 |
| C3×D3×Q16 | 3 |
| C2×C3×Dic12 | 3 |
| D3×Dic12 | 3 |