Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
464 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 85 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. C9×#944 | C2 | semidirect |
| 3. #11720893 | C2 | semidirect |
| 4. #11720581 | C2 | semidirect |
| 5. #11720260 | C2 | semidirect |
| 81. #944 | D9 | semidirect |
| 170. C3×C9 | #456 | semidirect |
| 241. C9 | #5246 | semidirect |
| 272. C3 | #10588775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63713 | 2 |
| C9×#944 | 2 |
| #11720893 | 2 |
| #11720581 | 2 |
| #11720260 | 2 |
| #10591648 | 3 |
| #10588775 | 3 |