Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
740 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. C2×#88547 | C2 | semidirect |
| 5. #11720527 | C2 | semidirect |
| 68. C22×C3×C9 | Q16 | semidirect |
| 149. C22×C9 | #216 | semidirect |
| 161. C3×C9 | #451 | semidirect |
| 211. C22×C3 | #3674 | semidirect |
| 226. C9 | #5050 | semidirect |
| 250. C22 | #88547 | semidirect |
| 257. C3 | #10588726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6226 | 2 |
| C3×C9×C22⋊Q8 | 2 |
| C2×#88547 | 2 |
| #11720571 | 2 |
| #11720527 | 2 |
| #10592749 | 3 |
| #10588726 | 3 |