Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
342 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 342 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. C9×#909 | C2 | semidirect |
| 2. C2×#88425 | C2 | semidirect |
| 4. #11720878 | C2 | semidirect |
| 5. #11720555 | C2 | semidirect |
| 6. C3×#63383 | C2 | semidirect |
| 7. #11720299 | C2 | semidirect |
| 37. #63383 | D3 | semidirect |
| 105. #909 | D9 | semidirect |
| 215. C3×C9 | #471 | semidirect |
| 299. C9 | #4748 | semidirect |
| 335. C3 | #10588884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#909 | 2 |
| C2×#88425 | 2 |
| #11720882 | 2 |
| #11720878 | 2 |
| #11720555 | 2 |
| C3×#63383 | 2 |
| #11720299 | 2 |
| #10590979 | 3 |
| #10588884 | 3 |