Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
770 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 121 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×Dic3×H(3,𝔽3) | C2 | semidirect |
| 4. Dic3×#272 | C2 | direct (N × H) |
| 8. C2×C3×#272 | C4 | semidirect |
| 10. C3⋊#1084 | C22 | semidirect |
| 11. Dic3×H(3,𝔽3) | C22 | semidirect |
| 14. C2×C32×Dic3 | D3 | semidirect |
| 21. C2×C3×H(3,𝔽3) | C2×C4 | semidirect |
| 23. C3×#272 | C2×C4 | semidirect |
| 31. C32×Dic3 | C2×D3 | semidirect |
| 34. C2×#272 | Dic3 | direct (N × H) |
| 39. C3×H(3,𝔽3) | C22×C4 | semidirect |
| 54. C2×C33 | C4×D3 | semidirect |
| 59. C2×H(3,𝔽3) | C2×Dic3 | semidirect |
| 61. #272 | C2×Dic3 | direct (N × H) |
| 85. C33 | C2×C4×D3 | semidirect |
| 87. H(3,𝔽3) | C22×Dic3 | semidirect |
| 100. C2×Dic3 | #272 | direct (N × H) |
| 109. C2×C32 | D3×Dic3 | semidirect |
| 136. Dic3 | C2×#272 | direct (N × H) |
| 140. C32 | C2×D3×Dic3 | semidirect |
| 155. C2×C3 | C4×#272 | semidirect |
| 168. C3 | C2×C4×#272 | semidirect |
| 171. C2 | Dic3×#272 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#272 | 2 |
| C2×C3⋊#1084 | 2 |
| C2×Dic3×H(3,𝔽3) | 2 |
| Dic3×#272 | 2 |
| C2×C3×D3×Dic3 | 3 |
| C2×C4×#272 | 3 |