Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
398 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 87 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. #11720930 | C2 | semidirect |
| 5. #11720537 | C2 | semidirect |
| 6. C3×#63376 | C2 | semidirect |
| 7. #11720297 | C2 | semidirect |
| 35. #63376 | D3 | semidirect |
| 92. C3⋊Dic9 | SD16 | semidirect |
| 216. C3×C9 | #461 | semidirect |
| 307. C9 | #4818 | semidirect |
| 347. C3 | #10588842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#204 | 2 |
| #11721025 | 2 |
| #11720930 | 2 |
| C2×#88423 | 2 |
| #11720537 | 2 |
| C3×#63376 | 2 |
| #11720297 | 2 |
| #10590748 | 3 |
| #10588842 | 3 |