Finite Group DatabasebetaFinite Group Databasebeta← C4⋊(C3⋊(C3⋊SL(2,ℤ/4))) #13173062
Order 1728.
1070 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1070 conjugacy classes of subgroups — too many to draw. Only its 275 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 |
|---|---|---|
| 6. C32×C4×A4 | C4 | semidirect |
| 28. C22×C32×C4 | Dic3 | semidirect |
| 31. C3×C4×A4 | Dic3 | semidirect |
| 40. C32×A4 | C4⋊C4 | semidirect |
| 83. C22×C3×C4 | C3⋊Dic3 | semidirect |
| 86. C4×A4 | C3⋊Dic3 | semidirect |
| 105. C22×C32 | C4⋊Dic3 | semidirect |
| 107. C3×A4 | C4⋊Dic3 | semidirect |
| 110. C32×C4 | SL(2,ℤ/4) | semidirect |
| 160. C22×C4 | C3⋊(C3⋊Dic3) | semidirect |
| 177. C22×C3 | C4⋊(C3⋊Dic3) | semidirect |
| 179. A4 | C4⋊(C3⋊Dic3) | semidirect |
| 182. C3×C4 | C3⋊SL(2,ℤ/4) | semidirect |
| 187. C32 | C4⋊SL(2,ℤ/4) | semidirect |
| 227. C22 | C4⋊(C3⋊(C3⋊Dic3)) | semidirect |
| 232. C4 | C3⋊(C3⋊SL(2,ℤ/4)) | semidirect |
| 234. C3 | C4⋊(C3⋊SL(2,ℤ/4)) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×A4 | 2 |
| C2×C3⋊(C3⋊SL(2,ℤ/4)) | 2 |
| C4⋊(C3⋊SL(2,ℤ/4)) | 3 |
| #10592911 | 3 |
| C4⋊(C3⋊(C3⋊Dic3)) | 4 |