Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
314 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 93 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×#812 | C2 | semidirect |
| 3. C2×C3×C9⋊C16 | C2 | semidirect |
| 4. #11720231 | C2 | semidirect |
| 5. (C3⋊D9)⋊C16 | C2 | semidirect |
| 24. C2×C9⋊C16 | D3 | semidirect |
| 68. #812 | D9 | semidirect |
| 143. C3×C9 | #504 | semidirect |
| 202. C9 | #4901 | semidirect |
| 226. C3 | #10588587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721770 | 2 |
| C9×#812 | 2 |
| C2×C3×C9⋊C16 | 2 |
| #11720231 | 2 |
| (C3⋊D9)⋊C16 | 2 |
| #10590624 | 3 |
| #10588587 | 3 |