Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
431 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 431 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 7. C4×C9×A4 | C4 | semidirect |
| 35. C22×C4×C9 | Dic3 | semidirect |
| 38. C4×C22⋊C9 | Dic3 | semidirect |
| 47. C9×A4 | C4⋊C4 | semidirect |
| 98. C4×A4 | Dic9 | semidirect |
| 121. C22×C9 | C4⋊Dic3 | semidirect |
| 123. C22⋊C9 | C4⋊Dic3 | semidirect |
| 126. C4×C9 | SL(2,ℤ/4) | semidirect |
| 179. C22×C4 | C3⋊Dic9 | semidirect |
| 198. A4 | C4⋊Dic9 | semidirect |
| 207. C9 | C4⋊SL(2,ℤ/4) | semidirect |
| 247. C22 | C4⋊(C3⋊Dic9) | semidirect |
| 252. C4 | C9⋊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×C4×C9×A4 | 2 |
| C2×C9⋊SL(2,ℤ/4) | 2 |
| C4⋊(C3⋊SL(2,ℤ/4)) | 3 |
| C4⋊((C22⋊C9)⋊C4) | 3 |
| #10588892 | 3 |
| C4⋊(C3⋊Dic9) | 4 |