Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
470 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 470 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. #11720575 | C2 | semidirect |
| 6. C23×C3⋊D9 | C4 | semidirect |
| 10. #88551 | C4 | semidirect |
| 17. C9×#99 | D3 | semidirect |
| 61. C3×#99 | D9 | semidirect |
| 135. #99 | C3⋊D9 | semidirect |
| 136. C3×C9 | AΣL(1,𝔽16) | semidirect |
| 203. C9 | #4471 | semidirect |
| 238. C3 | #10588150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721837 | 2 |
| C3×C9×#99 | 2 |
| #11720575 | 2 |
| #10589337 | 3 |
| #10588150 | 3 |