Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
464 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 464 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 |
|---|---|---|
| 2. C3×#63506 | C2 | semidirect |
| 3. #11720887 | C2 | semidirect |
| 4. #11720581 | C2 | semidirect |
| 5. #11720301 | C2 | semidirect |
| 26. #63506 | D3 | semidirect |
| 170. C3×C9 | #456 | semidirect |
| 241. C9 | #5095 | semidirect |
| 272. C3 | #10588925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#1007 | 2 |
| C3×#63506 | 2 |
| #11720887 | 2 |
| #11720581 | 2 |
| #11720301 | 2 |
| #10591648 | 3 |
| #10588925 | 3 |