Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
650 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 1. C2×C3×C9×Q16 | C2 | semidirect |
| 2. #11721857 | C2 | semidirect |
| 3. C2×#88548 | C2 | semidirect |
| 5. C8×C3⋊Dic9 | C2 | semidirect |
| 22. C2×C9×Q16 | D3 | semidirect |
| 64. C2×C3×Q16 | D9 | semidirect |
| 130. C2×Q16 | C3⋊D9 | semidirect |
| 135. C3×C9 | #495 | semidirect |
| 186. C9 | #5191 | semidirect |
| 210. C3 | #10588871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×Q16 | 2 |
| #11721857 | 2 |
| C2×#88548 | 2 |
| C2×#88525 | 2 |
| C8×C3⋊Dic9 | 2 |
| #10592890 | 3 |
| #10588871 | 3 |