Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
276 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 65 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. C9×#919 | C2 | semidirect |
| 2. #11720811 | C2 | semidirect |
| 3. #11720568 | C2 | semidirect |
| 4. C3×#63387 | C2 | semidirect |
| 5. #11720241 | C2 | semidirect |
| 6. #11720238 | C2 | semidirect |
| 7. D3×C9⋊C16 | C2 | semidirect |
| 32. #63387 | D3 | semidirect |
| 82. #919 | D9 | semidirect |
| 175. C3×C9 | #508 | semidirect |
| 240. C9 | #4916 | semidirect |
| 269. C3 | #10588874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#919 | 2 |
| #11720811 | 2 |
| #11720568 | 2 |
| C3×#63387 | 2 |
| #11720241 | 2 |
| #11720238 | 2 |
| D3×C9⋊C16 | 2 |
| #10591046 | 3 |
| #10588874 | 3 |