Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
369 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 369 conjugacy classes of subgroups — too many to draw. Only its 60 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. C2×#66362 | C2 | direct (N × H) |
| 2. C24×H(3,𝔽3) | C3 | semidirect |
| 3. C22×C22⋊H(3,𝔽3) | C3 | semidirect |
| 4. C22×C3×C22⋊C9 | C3 | semidirect |
| 6. #66362 | C22 | direct (N × H) |
| 9. C23×H(3,𝔽3) | C2×C3 | semidirect |
| 10. C2×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 11. C2×C3×C22⋊C9 | C2×C3 | semidirect |
| 22. C22×H(3,𝔽3) | A4 | semidirect |
| 23. C22×H(3,𝔽3) | C22×C3 | semidirect |
| 25. C22⋊H(3,𝔽3) | C22×C3 | semidirect |
| 26. C3×C22⋊C9 | C22×C3 | semidirect |
| 39. C2×H(3,𝔽3) | C2×A4 | semidirect |
| 62. H(3,𝔽3) | C22×A4 | semidirect |
| 82. C24 | #732 | semidirect |
| 109. C23 | C2×#732 | semidirect |
| 124. C22 | #66362 | direct (N × H) |
| 125. C22 | C22×#732 | semidirect |
| 132. C2 | C2×#66362 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66362 | 2 |
| C24×H(3,𝔽3) | 3 |
| C22×C22⋊H(3,𝔽3) | 3 |
| C22×C3×C22⋊C9 | 3 |
| C22×#732 | 4 |