Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
432 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#88547 | C2 | semidirect |
| 3. C2×C3×#3674 | C2 | semidirect |
| 4. #11720932 | C2 | semidirect |
| 7. #11720258 | C2 | semidirect |
| 33. C2×#3674 | D3 | semidirect |
| 214. C3×C9 | #497 | semidirect |
| 301. C9 | #5190 | semidirect |
| 336. C3 | #10588737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88547 | 2 |
| C9×#947 | 2 |
| C2×C3×#3674 | 2 |
| #11720932 | 2 |
| C2×#88424 | 2 |
| C2×#88423 | 2 |
| #11720258 | 2 |
| #10591627 | 3 |
| #10588737 | 3 |