Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. D3×#3667 | C2 | semidirect |
| 3. #11720581 | C2 | semidirect |
| 4. C3×#63394 | C2 | semidirect |
| 5. #11720296 | C2 | semidirect |
| 28. #63394 | D3 | semidirect |
| 177. C3×C9 | #413 | semidirect |
| 254. C9 | #4751 | semidirect |
| 289. C3 | #10588915 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#239 | 2 |
| D3×#3667 | 2 |
| #11720581 | 2 |
| C3×#63394 | 2 |
| #11720296 | 2 |
| #10591637 | 3 |
| #10588915 | 3 |