Finite Group DatabasebetaFinite Group Databasebeta← H(3,𝔽3)×C3⋊AGL(1,ℤ/9) #72243662
Order 4374.
4843 conjugacy classes of subgroups; only the 252 normal subgroups are shown.
This group has 4843 conjugacy classes of subgroups — too many to draw. Only its 252 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. C3×H(3,𝔽3)×3−1+2 | C2 | semidirect |
| 2. C32×C3⋊AGL(1,ℤ/9) | C3 | semidirect |
| 5. C3⋊(D9⋊H(3,𝔽3)) | C3 | semidirect |
| 6. H(3,𝔽3)×C3⋊D9 | C3 | semidirect |
| 7. C33×3−1+2 | C2×C3 | semidirect |
| 12. H(3,𝔽3)×3−1+2 | D3 | semidirect |
| 14. C3×C9⋊H(3,𝔽3) | C2×C3 | semidirect |
| 17. C3×C9×H(3,𝔽3) | C2×C3 | semidirect |
| 21. C3×C3⋊AGL(1,ℤ/9) | C32 | semidirect |
| 24. C32×C3⋊D9 | C32 | semidirect |
| 39. C32×3−1+2 | C3×D3 | semidirect |
| 41. C32×3−1+2 | C2×C32 | semidirect |
| 51. C33×C9 | C2×C32 | semidirect |
| 57. C9⋊H(3,𝔽3) | C3×D3 | semidirect |
| 65. C9×H(3,𝔽3) | C3×D3 | semidirect |
| 77. C3⋊AGL(1,ℤ/9) | H(3,𝔽3) | direct (N × H) |
| 123. C3×3−1+2 | C2×H(3,𝔽3) | semidirect |
| 125. C3×3−1+2 | C32×D3 | semidirect |
| 140. C3×H(3,𝔽3) | AGL(1,ℤ/9) | semidirect |
| 154. C32×C9 | C32×D3 | semidirect |
| 177. C3⋊D9 | C3×H(3,𝔽3) | semidirect |
| 215. C33 | C3×AGL(1,ℤ/9) | semidirect |
| 231. 3−1+2 | D3×H(3,𝔽3) | semidirect |
| 240. H(3,𝔽3) | C3⋊AGL(1,ℤ/9) | direct (N × H) |
| 258. C3×C9 | C2×C3×H(3,𝔽3) | semidirect |
| 310. C32 | C3×C3⋊AGL(1,ℤ/9) | semidirect |
| 316. C9 | C3×D3×H(3,𝔽3) | semidirect |
| 332. C3 | H(3,𝔽3)×AGL(1,ℤ/9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×H(3,𝔽3)×3−1+2 | 2 |
| C32×C3⋊AGL(1,ℤ/9) | 3 |
| C3×C3⋊D3×H(3,𝔽3) | 3 |
| H(3,𝔽3)×AGL(1,ℤ/9) | 3 |
| C3⋊(D9⋊H(3,𝔽3)) | 3 |
| H(3,𝔽3)×C3⋊D9 | 3 |