Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
386 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11721865 | C2 | semidirect |
| 2. C9×#949 | C2 | semidirect |
| 3. C3×#63512 | C2 | semidirect |
| 4. C2×#88421 | C2 | semidirect |
| 5. #11720296 | C2 | semidirect |
| 6. #11720287 | C2 | semidirect |
| 7. #11720286 | C2 | semidirect |
| 33. #63512 | D3 | semidirect |
| 105. #949 | D9 | semidirect |
| 228. C3×C9 | #472 | semidirect |
| 322. C9 | #5199 | semidirect |
| 362. C3 | #10588880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721865 | 2 |
| C9×#949 | 2 |
| C3×#63512 | 2 |
| C2×#88421 | 2 |
| #11720296 | 2 |
| #11720287 | 2 |
| #11720286 | 2 |
| #10591678 | 3 |
| #10588880 | 3 |