Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
908 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 216 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 |
|---|---|---|
| 49. C33×C4 | Q16 | semidirect |
| 104. C32×C4 | #216 | semidirect |
| 105. C32×C4 | #216 | semidirect |
| 115. C33 | #494 | semidirect |
| 153. C3×C4 | #3718 | semidirect |
| 154. C3×C4 | #3756 | semidirect |
| 160. C32 | #5092 | semidirect |
| 161. C32 | #5092 | semidirect |
| 178. C4 | #88798 | semidirect |
| 181. C3 | #10590387 | semidirect |
| 182. C3 | #10592791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64078 | 2 |
| C32×#869 | 2 |
| C2×#88798 | 2 |
| C4×C3⋊(C3⋊(C3⋊C8)) | 2 |
| #10592791 | 3 |
| #10590387 | 3 |