Finite Group DatabasebetaFinite Group Databasebeta← C2×C4⋊(C3⋊AGL(1,𝔽9)) #13180939
Order 1728.
346 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 3. C4⋊(C3⋊AGL(1,𝔽9)) | C2 | direct (N × H) |
| 23. C2×C33×C4 | C8 | semidirect |
| 24. C2×C3×C3⋊Dic3 | C8 | semidirect |
| 25. C3×C4×C3⋊D3 | C8 | semidirect |
| 45. C33×C4 | C2×C8 | semidirect |
| 46. C3×C3⋊Dic3 | C2×C8 | semidirect |
| 61. C2×C32×C4 | C3⋊C8 | semidirect |
| 62. C2×C3⋊Dic3 | C3⋊C8 | semidirect |
| 63. C4×C3⋊D3 | C3⋊C8 | semidirect |
| 69. C2×C33 | C4⋊C8 | semidirect |
| 71. C3×C3⋊D3 | C4⋊C8 | semidirect |
| 99. C32×C4 | C2×C3⋊C8 | semidirect |
| 100. C3⋊Dic3 | C2×C3⋊C8 | semidirect |
| 105. C33 | C2×C4⋊C8 | semidirect |
| 119. C2×C3×C4 | AGL(1,𝔽9) | semidirect |
| 128. C2×C32 | C4⋊(C3⋊C8) | semidirect |
| 130. C3⋊D3 | C4⋊(C3⋊C8) | semidirect |
| 161. C3×C4 | C2×AGL(1,𝔽9) | semidirect |
| 165. C32 | C2×C4⋊(C3⋊C8) | semidirect |
| 176. C2×C4 | C3⋊AGL(1,𝔽9) | semidirect |
| 185. C2×C3 | C4⋊AGL(1,𝔽9) | semidirect |
| 200. C4 | C2×C3⋊AGL(1,𝔽9) | semidirect |
| 203. C3 | C2×C4⋊AGL(1,𝔽9) | semidirect |
| 207. C2 | C4⋊(C3⋊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×C3⋊AGL(1,𝔽9) | 2 |
| C2×C3×C4×#157 | 2 |
| C4⋊(C3⋊AGL(1,𝔽9)) | 2 |
| C2×C4⋊AGL(1,𝔽9) | 3 |
| C2×C4⋊(C3⋊C8) | 9 |