Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
770 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 105 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. C22×C3×#272 | C2 | semidirect |
| 2. C22×D3×H(3,𝔽3) | C2 | semidirect |
| 3. C2×C3⋊#1084 | C2 | semidirect |
| 4. #10619891 | C2 | direct (N × H) |
| 9. C2×C3×#272 | C22 | semidirect |
| 11. C2×D3×H(3,𝔽3) | C22 | semidirect |
| 12. C3⋊#1084 | C22 | semidirect |
| 14. C22×C32×D3 | D3 | semidirect |
| 18. C22×#272 | D3 | semidirect |
| 22. C2×C3×H(3,𝔽3) | D4 | semidirect |
| 33. C2×C32×D3 | C2×D3 | semidirect |
| 40. C2×#272 | C2×D3 | semidirect |
| 43. C3×H(3,𝔽3) | C2×D4 | semidirect |
| 58. C2×C33 | #67 | semidirect |
| 65. C2×H(3,𝔽3) | #67 | semidirect |
| 94. C33 | C2×#67 | semidirect |
| 96. H(3,𝔽3) | C2×#67 | semidirect |
| 103. C22×D3 | #272 | semidirect |
| 119. C2×C32 | #625 | semidirect |
| 147. C2×D3 | C2×#272 | semidirect |
| 155. C32 | C2×#625 | semidirect |
| 172. C2×C3 | #6235 | semidirect |
| 187. C3 | C2×#6235 | semidirect |
| 191. C2 | #10619891 | 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 |
| C22×D3×H(3,𝔽3) | 2 |
| C2×C3⋊#1084 | 2 |
| #10619891 | 2 |
| C2×C3×#625 | 3 |
| C2×#6235 | 3 |