Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
710 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 195 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 |
|---|---|---|
| 2. C2×#88543 | C2 | semidirect |
| 3. #11721706 | C2 | semidirect |
| 4. C4×C3⋊(C9⋊C8) | C2 | semidirect |
| 29. C3⋊(C9⋊C8) | D4 | semidirect |
| 49. C3×C4×C9 | SD16 | semidirect |
| 103. C4×C9 | #214 | semidirect |
| 110. C3×C9 | #492 | semidirect |
| 146. C3×C4 | #3672 | semidirect |
| 153. C9 | #5076 | semidirect |
| 172. C4 | #88543 | semidirect |
| 174. C3 | #10588753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#127 | 2 |
| C2×#88543 | 2 |
| #11721706 | 2 |
| C4×C3⋊(C9⋊C8) | 2 |
| #10592775 | 3 |
| #10588753 | 3 |