Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
430 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 85 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. C3×C9×#99 | C2 | semidirect |
| 3. #11720577 | C2 | semidirect |
| 9. C2×C4⋊(C3⋊D9) | C4 | semidirect |
| 12. C4×C3⋊Dic9 | C4 | semidirect |
| 17. C9×#99 | D3 | semidirect |
| 60. C3×#99 | D9 | semidirect |
| 132. #99 | C3⋊D9 | semidirect |
| 133. C3×C9 | #353 | semidirect |
| 198. C9 | #4474 | semidirect |
| 232. C3 | #10588151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721840 | 2 |
| C3×C9×#99 | 2 |
| #11720577 | 2 |
| #10589340 | 3 |
| #10588151 | 3 |