Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
699 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 699 conjugacy classes of subgroups — too many to draw. Only its 99 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⋊((C3⋊Dic3)⋊C3) | C2 | semidirect |
| 3. #10619903 | C2 | direct (N × H) |
| 7. C2×C3×#272 | C4 | semidirect |
| 9. C3⋊((C3⋊Dic3)⋊C3) | C22 | semidirect |
| 12. C2×C3⋊(C3⋊Dic3) | D3 | semidirect |
| 19. C2×C3×H(3,𝔽3) | C2×C4 | semidirect |
| 21. C3×#272 | C2×C4 | semidirect |
| 31. C3⋊(C3⋊Dic3) | C2×D3 | semidirect |
| 36. C2×#272 | Dic3 | semidirect |
| 40. C3×H(3,𝔽3) | C22×C4 | semidirect |
| 57. C2×C33 | C4×D3 | semidirect |
| 65. C2×H(3,𝔽3) | C2×Dic3 | semidirect |
| 67. #272 | C2×Dic3 | semidirect |
| 95. C33 | C2×C4×D3 | semidirect |
| 98. H(3,𝔽3) | C22×Dic3 | semidirect |
| 122. C2×C32 | D3×Dic3 | semidirect |
| 155. C32 | C2×D3×Dic3 | semidirect |
| 170. C2×C3 | #6199 | semidirect |
| 184. C3 | C2×#6199 | semidirect |
| 187. C2 | #10619903 | 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⋊((C3⋊Dic3)⋊C3) | 2 |
| #10619903 | 2 |
| C2×D3×C3⋊Dic3 | 3 |
| C2×#6199 | 3 |