Finite Group DatabasebetaFinite Group Databasebeta← C2×(C2×D3)⋊AGL(1,𝔽9) #13180366
Order 1728.
570 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 100 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. C22×C3⋊AGL(1,𝔽9) | C2 | semidirect |
| 3. C22×C3×AGL(1,𝔽9) | C2 | semidirect |
| 4. (C2×D3)⋊AGL(1,𝔽9) | C2 | direct (N × H) |
| 14. C2×C3⋊AGL(1,𝔽9) | C22 | semidirect |
| 16. C2×C3×AGL(1,𝔽9) | C22 | semidirect |
| 19. C22×AGL(1,𝔽9) | D3 | semidirect |
| 21. C22×C3⋊(C3⋊D3) | C8 | semidirect |
| 23. C22×C32×D3 | C8 | semidirect |
| 26. C2×D3×C3⋊D3 | C8 | semidirect |
| 51. C2×AGL(1,𝔽9) | C2×D3 | semidirect |
| 54. C2×C3⋊(C3⋊D3) | C2×C8 | semidirect |
| 60. C2×C32×D3 | C2×C8 | semidirect |
| 99. C2×C33 | C22⋊C8 | semidirect |
| 102. C3×C3⋊D3 | C22⋊C8 | semidirect |
| 153. C33 | C2×C22⋊C8 | semidirect |
| 168. C22×D3 | AGL(1,𝔽9) | semidirect |
| 185. C2×C32 | (C2×D3)⋊C8 | semidirect |
| 190. C3⋊D3 | (C2×D3)⋊C8 | semidirect |
| 234. C2×D3 | C2×AGL(1,𝔽9) | semidirect |
| 241. C32 | C2×(C2×D3)⋊C8 | semidirect |
| 268. C2×C3 | C22⋊AGL(1,𝔽9) | semidirect |
| 295. C3 | C2×C22⋊AGL(1,𝔽9) | semidirect |
| 301. C2 | (C2×D3)⋊AGL(1,𝔽9) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×#157 | 2 |
| C22×C3⋊AGL(1,𝔽9) | 2 |
| C22×C3×AGL(1,𝔽9) | 2 |
| (C2×D3)⋊AGL(1,𝔽9) | 2 |
| C2×C22⋊AGL(1,𝔽9) | 3 |
| C2×(C2×D3)⋊C8 | 9 |