Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
400 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 73 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×#88544 | C2 | semidirect |
| 2. C9×#932 | C2 | semidirect |
| 3. #11720885 | C2 | semidirect |
| 4. #11720878 | C2 | semidirect |
| 5. C3×#63391 | C2 | semidirect |
| 6. #11720288 | C2 | semidirect |
| 7. #11720286 | C2 | semidirect |
| 37. #63391 | D3 | semidirect |
| 105. #932 | D9 | semidirect |
| 231. C3×C9 | #472 | semidirect |
| 329. C9 | #4749 | semidirect |
| 370. C3 | #10588880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88544 | 2 |
| C9×#932 | 2 |
| #11720885 | 2 |
| #11720878 | 2 |
| C3×#63391 | 2 |
| #11720288 | 2 |
| #11720286 | 2 |
| #10591508 | 3 |
| #10588880 | 3 |