Finite Group DatabasebetaFinite Group Databasebeta← C2×H(3,𝔽3)⋊(C22⋊C9) #14516624
Order 1944.
412 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 64 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. H(3,𝔽3)⋊(C22⋊C9) | C2 | direct (N × H) |
| 3. C2×C32×C22⋊C9 | C3 | semidirect |
| 4. C2×C32⋊(C22⋊C9) | C3 | semidirect |
| 9. C32×C22⋊C9 | C2×C3 | semidirect |
| 10. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 15. C23×H(3,𝔽3) | C9 | semidirect |
| 35. C22×H(3,𝔽3) | C2×C9 | semidirect |
| 65. C2×H(3,𝔽3) | C22⋊C9 | semidirect |
| 104. H(3,𝔽3) | C2×C22⋊C9 | semidirect |
| 180. C23 | H(3,𝔽3)⋊C9 | semidirect |
| 204. C22 | C2×H(3,𝔽3)⋊C9 | semidirect |
| 214. C2 | H(3,𝔽3)⋊(C22⋊C9) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)⋊(C22⋊C9) | 2 |
| C23×C3×H(3,𝔽3) | 3 |
| C2×C32×C22⋊C9 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×H(3,𝔽3)⋊C9 | 4 |