Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
306 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 1. C3×#3797 | C2 | semidirect |
| 3. C3×#3743 | C2 | semidirect |
| 4. C32×Dic12 | C2 | semidirect |
| 5. C32×#204 | C2 | semidirect |
| 6. C3×#3718 | C2 | semidirect |
| 7. C3×#3715 | C2 | semidirect |
| 10. #63811 | C3 | direct (N × H) |
| 26. #3797 | C2×C3 | semidirect |
| 30. #3743 | C2×C3 | semidirect |
| 36. C3×Dic12 | D3 | semidirect |
| 37. C3×Dic12 | C2×C3 | semidirect |
| 39. C3×#204 | D3 | semidirect |
| 40. C3×#204 | C2×C3 | semidirect |
| 44. #3718 | C2×C3 | semidirect |
| 45. #3715 | C2×C3 | semidirect |
| 121. Dic12 | C3×D3 | semidirect |
| 122. #204 | C3×D3 | semidirect |
| 158. C33 | #137 | semidirect |
| 259. C32 | #915 | semidirect |
| 260. C32 | #918 | semidirect |
| 261. C32 | C3×#137 | semidirect |
| 299. C3 | #63811 | direct (N × H) |
| 300. C3 | C3×#915 | semidirect |
| 301. C3 | C3×#918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3797 | 2 |
| C3×#3796 | 2 |
| C3×#3743 | 2 |
| C32×Dic12 | 2 |
| C32×#204 | 2 |
| C3×#3718 | 2 |
| C3×#3715 | 2 |
| C3×#918 | 3 |
| C3×#915 | 3 |
| #63811 | 3 |