Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
366 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 51 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. C9×#834 | C2 | semidirect |
| 3. C3×#63393 | C2 | semidirect |
| 9. C2×C4⋊(C3⋊D9) | C4 | semidirect |
| 10. C4×C3⋊Dic9 | C4 | semidirect |
| 19. #63393 | D3 | semidirect |
| 70. #834 | D9 | semidirect |
| 164. C3×C9 | #353 | semidirect |
| 254. C9 | #4474 | semidirect |
| 294. C3 | #10588151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721840 | 2 |
| C9×#834 | 2 |
| C3×#63393 | 2 |
| #10589179 | 3 |
| #10588151 | 3 |