Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
866 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 866 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×C3×#272 | C2 | semidirect |
| 3. C2×Dic3×H(3,𝔽3) | C2 | semidirect |
| 4. #10619893 | C2 | direct (N × H) |
| 9. C2×C3⋊#272 | C22 | semidirect |
| 11. C2×C3×#272 | C22 | semidirect |
| 12. Dic3×H(3,𝔽3) | C22 | semidirect |
| 15. C2×C32×Dic3 | D3 | semidirect |
| 19. C22×#272 | D3 | semidirect |
| 22. C2×C3×H(3,𝔽3) | D4 | semidirect |
| 34. C32×Dic3 | C2×D3 | semidirect |
| 42. C2×#272 | C2×D3 | semidirect |
| 44. C3×H(3,𝔽3) | C2×D4 | semidirect |
| 59. C2×C33 | D12 | semidirect |
| 65. C2×H(3,𝔽3) | #67 | semidirect |
| 97. C33 | C2×D12 | semidirect |
| 99. H(3,𝔽3) | C2×#67 | semidirect |
| 112. C2×Dic3 | #272 | semidirect |
| 121. C2×C32 | #626 | semidirect |
| 156. Dic3 | C2×#272 | semidirect |
| 160. C32 | C2×#626 | semidirect |
| 176. C2×C3 | C4⋊#272 | semidirect |
| 193. C3 | C2×C4⋊#272 | semidirect |
| 197. C2 | #10619893 | 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×C3×#272 | 2 |
| C2×Dic3×H(3,𝔽3) | 2 |
| #10619893 | 2 |
| C2×C3×#626 | 3 |
| C2×C4⋊#272 | 3 |