Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
570 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 84 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. C2×D3×AGL(1,𝔽9) | C2 | semidirect |
| 3. #11724243 | C2 | semidirect |
| 4. C3×C22⋊AGL(1,𝔽9) | C2 | semidirect |
| 5. (C2×D3)⋊AGL(1,𝔽9) | C2 | semidirect |
| 15. C2×C3⋊AGL(1,𝔽9) | C22 | semidirect |
| 16. C2×C3×AGL(1,𝔽9) | C22 | semidirect |
| 22. C22⋊AGL(1,𝔽9) | D3 | direct (N × H) |
| 23. C22×C3⋊(C3⋊D3) | C8 | semidirect |
| 25. C22×C32×D3 | C8 | semidirect |
| 28. C2×D3×C3⋊D3 | C8 | semidirect |
| 29. C2×D3×C3⋊D3 | C8 | semidirect |
| 56. C2×AGL(1,𝔽9) | C2×D3 | semidirect |
| 57. C22×C33 | C2×C8 | semidirect |
| 60. C2×C3⋊(C3⋊D3) | C2×C8 | semidirect |
| 63. C2×C3×C3⋊D3 | C2×C8 | semidirect |
| 67. C2×C32×D3 | C2×C8 | semidirect |
| 118. C3⋊(C3⋊D3) | C22⋊C8 | semidirect |
| 123. C32×D3 | C22⋊C8 | semidirect |
| 141. C22×C32 | D3×C8 | semidirect |
| 159. C2×C3⋊D3 | D3×C8 | semidirect |
| 183. C33 | C2×C22⋊C8 | semidirect |
| 202. C22×D3 | AGL(1,𝔽9) | semidirect |
| 257. C22×C3 | C2×AGL(1,𝔽9) | semidirect |
| 285. C2×D3 | C2×AGL(1,𝔽9) | semidirect |
| 292. C32 | D3×C22⋊C8 | semidirect |
| 335. D3 | C22⋊AGL(1,𝔽9) | direct (N × H) |
| 352. C22 | D3×AGL(1,𝔽9) | semidirect |
| 359. C3 | C2×C22⋊AGL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×#157 | 2 |
| C2×D3×AGL(1,𝔽9) | 2 |
| #11724243 | 2 |
| C3×C22⋊AGL(1,𝔽9) | 2 |
| (C2×D3)⋊AGL(1,𝔽9) | 2 |
| C2×C22⋊AGL(1,𝔽9) | 3 |
| D3×C22⋊C8 | 9 |