Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
338 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 70 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. C22×C3⋊AGL(1,𝔽9) | C2 | semidirect |
| 2. C2×D3×AGL(1,𝔽9) | C2 | semidirect |
| 4. C3×C22⋊AGL(1,𝔽9) | C2 | semidirect |
| 5. Dic3⋊AGL(1,𝔽9) | C2 | semidirect |
| 6. (C2×D3)⋊AGL(1,𝔽9) | C2 | semidirect |
| 7. Dic3×AGL(1,𝔽9) | C2 | semidirect |
| 26. C22⋊AGL(1,𝔽9) | D3 | semidirect |
| 40. C3⋊AGL(1,𝔽9) | D4 | semidirect |
| 43. #6312 | C8 | semidirect |
| 44. C32×#67 | C8 | semidirect |
| 45. #6292 | C8 | semidirect |
| 46. #6290 | C8 | semidirect |
| 63. C22×C33 | C2×C8 | semidirect |
| 64. C2×C3⋊(C3⋊D3) | C2×C8 | semidirect |
| 67. C2×C3×C3⋊D3 | C2×C8 | semidirect |
| 69. C2×C32×D3 | C2×C8 | semidirect |
| 77. C3⋊(C3⋊Dic3) | C2×C8 | semidirect |
| 78. C32×Dic3 | C2×C8 | semidirect |
| 138. C22×C32 | D3×C8 | semidirect |
| 146. C2×C3⋊D3 | D3×C8 | semidirect |
| 172. C33 | C8×D4 | semidirect |
| 188. #67 | AGL(1,𝔽9) | semidirect |
| 237. C22×C3 | C2×AGL(1,𝔽9) | semidirect |
| 249. C2×D3 | C2×AGL(1,𝔽9) | semidirect |
| 259. Dic3 | C2×AGL(1,𝔽9) | semidirect |
| 262. C32 | #67⋊C8 | semidirect |
| 307. C22 | D3×AGL(1,𝔽9) | semidirect |
| 317. C3 | D4×AGL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊AGL(1,𝔽9) | 2 |
| C2×D3×AGL(1,𝔽9) | 2 |
| #67×#157 | 2 |
| C3×C22⋊AGL(1,𝔽9) | 2 |
| Dic3⋊AGL(1,𝔽9) | 2 |
| (C2×D3)⋊AGL(1,𝔽9) | 2 |
| Dic3×AGL(1,𝔽9) | 2 |
| D4×AGL(1,𝔽9) | 3 |
| #67⋊C8 | 9 |