Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
730 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 161 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⋊#1084 | C2 | semidirect |
| 3. C2×C3×#1084 | C2 | semidirect |
| 4. D3×#1084 | C2 | direct (N × H) |
| 8. C2×D3×H(3,𝔽3) | C4 | semidirect |
| 10. C3⋊#1084 | C22 | semidirect |
| 11. C3×#1084 | C22 | semidirect |
| 20. C2×#1084 | D3 | direct (N × H) |
| 21. C2×C3×H(3,𝔽3) | C2×C4 | semidirect |
| 23. D3×H(3,𝔽3) | C2×C4 | semidirect |
| 28. C2×C32×D3 | Dic3 | semidirect |
| 38. #1084 | C2×D3 | direct (N × H) |
| 39. C3×H(3,𝔽3) | C22×C4 | semidirect |
| 54. C2×C33 | C2×Dic3 | semidirect |
| 56. C32×D3 | C2×Dic3 | semidirect |
| 60. C2×H(3,𝔽3) | C4×D3 | semidirect |
| 84. C33 | C22×Dic3 | semidirect |
| 86. H(3,𝔽3) | C2×C4×D3 | semidirect |
| 108. C2×C32 | D3×Dic3 | semidirect |
| 124. C2×D3 | #1084 | direct (N × H) |
| 137. C32 | C2×D3×Dic3 | semidirect |
| 151. C2×C3 | C2×#1084 | semidirect |
| 155. D3 | C2×#1084 | direct (N × H) |
| 164. C3 | C22×#1084 | semidirect |
| 167. C2 | D3×#1084 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×H(3,𝔽3) | 2 |
| C2×C3⋊#1084 | 2 |
| C2×C3×#1084 | 2 |
| D3×#1084 | 2 |
| C2×C3×D3×Dic3 | 3 |
| C22×#1084 | 3 |