Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
790 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 790 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 |
|---|---|---|
| 1. C22×#6226 | C2 | semidirect |
| 3. C2×#88524 | C2 | semidirect |
| 4. C3×C9×C22⋊C8 | C2 | semidirect |
| 5. #11720539 | C2 | semidirect |
| 27. C9×C22⋊C8 | D3 | semidirect |
| 41. #6226 | D4 | semidirect |
| 69. C22×C3×C9 | SD16 | semidirect |
| 84. C3×C22⋊C8 | D9 | semidirect |
| 157. C22×C9 | #204 | semidirect |
| 170. C22⋊C8 | C3⋊D9 | semidirect |
| 171. C3×C9 | #448 | semidirect |
| 225. C22×C3 | #3664 | semidirect |
| 244. C9 | #4738 | semidirect |
| 274. C22 | #88524 | semidirect |
| 280. C3 | #10588404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6226 | 2 |
| #11721819 | 2 |
| C2×#88524 | 2 |
| C3×C9×C22⋊C8 | 2 |
| #11720539 | 2 |
| #10592437 | 3 |
| #10588404 | 3 |