Finite Group DatabasebetaFinite Group Databasebeta← (C3×AGL(1,ℤ/9))⋊A4 #14518207
Order 1944.
264 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 35 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. #11757857 | C2 | semidirect |
| 2. C22×C3×AGL(1,ℤ/9) | C3 | semidirect |
| 4. C3×A4×D9 | C3 | semidirect |
| 5. C3×D9⋊A4 | C3 | semidirect |
| 7. C22×C3×3−1+2 | C2×C3 | semidirect |
| 11. C3×C9⋊A4 | C2×C3 | semidirect |
| 12. C3×C9×A4 | C2×C3 | semidirect |
| 28. C3×AGL(1,ℤ/9) | A4 | semidirect |
| 53. C3×3−1+2 | C2×A4 | semidirect |
| 66. C22×D9 | H(3,𝔽3) | semidirect |
| 99. C3×A4 | AGL(1,ℤ/9) | semidirect |
| 102. C22×C9 | C2×H(3,𝔽3) | semidirect |
| 145. D9 | C22⋊H(3,𝔽3) | semidirect |
| 174. C9 | C2×C22⋊H(3,𝔽3) | semidirect |
| 190. C22 | D9⋊H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757857 | 2 |
| C22×C3×AGL(1,ℤ/9) | 3 |
| D3×C22⋊H(3,𝔽3) | 3 |
| C3×A4×D9 | 3 |
| C3×D9⋊A4 | 3 |
| D9⋊H(3,𝔽3) | 4 |