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×#88543 | C2 | semidirect |
| 4. #11720571 | C2 | semidirect |
| 5. #11720527 | C2 | semidirect |
| 41. #6226 | D4 | semidirect |
| 72. C22×C3×C9 | SD16 | semidirect |
| 160. C22×C9 | #214 | semidirect |
| 171. C3×C9 | #448 | semidirect |
| 231. C22×C3 | #3672 | semidirect |
| 244. C9 | #5040 | semidirect |
| 274. C22 | #88543 | semidirect |
| 280. C3 | #10588716 | 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×#121 | 2 |
| C2×#88543 | 2 |
| #11720571 | 2 |
| #11720527 | 2 |
| #10592739 | 3 |
| #10588716 | 3 |