Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
930 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 219 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. C2×#88534 | C2 | semidirect |
| 3. C3×C9×#95 | C2 | semidirect |
| 16. C9×#95 | D3 | semidirect |
| 51. C3×#95 | D9 | semidirect |
| 106. #95 | C3⋊D9 | semidirect |
| 107. C3×C9 | #396 | semidirect |
| 158. C9 | #4676 | semidirect |
| 185. C3 | #10588356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88536 | 2 |
| C2×#88534 | 2 |
| C3×C9×#95 | 2 |
| #10592375 | 3 |
| #10588356 | 3 |