Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
354 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 354 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×#908 | C2 | semidirect |
| 2. #11720882 | C2 | semidirect |
| 3. C2×#88421 | C2 | semidirect |
| 4. #11720878 | C2 | semidirect |
| 5. #11720555 | C2 | semidirect |
| 6. C3×#63383 | C2 | semidirect |
| 7. #11720296 | C2 | semidirect |
| 37. #63383 | D3 | semidirect |
| 106. #908 | D9 | semidirect |
| 219. C3×C9 | #472 | semidirect |
| 307. C9 | #4749 | semidirect |
| 346. C3 | #10588880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#908 | 2 |
| #11720882 | 2 |
| C2×#88421 | 2 |
| #11720878 | 2 |
| #11720555 | 2 |
| C3×#63383 | 2 |
| #11720296 | 2 |
| #10590982 | 3 |
| #10588880 | 3 |