Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
277 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 277 conjugacy classes of subgroups — too many to draw. Only its 49 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. C32×SL(2,ℤ/4) | C3 | semidirect |
| 4. A4×H(3,𝔽3) | C4 | semidirect |
| 15. C32×A4 | C3×C4 | semidirect |
| 19. C22×H(3,𝔽3) | Dic3 | semidirect |
| 36. SL(2,ℤ/4) | H(3,𝔽3) | direct (N × H) |
| 41. C22×C32 | C3×Dic3 | semidirect |
| 52. H(3,𝔽3) | SL(2,ℤ/4) | direct (N × H) |
| 78. A4 | C4×H(3,𝔽3) | semidirect |
| 88. C32 | C3×SL(2,ℤ/4) | semidirect |
| 103. C22 | Dic3×H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×A4×H(3,𝔽3) | 2 |
| C32×SL(2,ℤ/4) | 3 |
| C22⋊C4×H(3,𝔽3) | 3 |
| Dic3×H(3,𝔽3) | 4 |