Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
194 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 73 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. #11720534 | C2 | semidirect |
| 3. C2×C3×C9⋊C16 | C2 | semidirect |
| 19. C2×C9⋊C16 | D3 | semidirect |
| 113. C3×C9 | #350 | semidirect |
| 163. C9 | #4508 | semidirect |
| 186. C3 | #10588238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#901 | 2 |
| #11720534 | 2 |
| C2×C3×C9⋊C16 | 2 |
| #10589112 | 3 |
| #10588238 | 3 |