Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
380 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11720935 | C2 | semidirect |
| 3. #11720576 | C2 | semidirect |
| 4. C9×#832 | C2 | semidirect |
| 5. #11720283 | C2 | semidirect |
| 6. #11720274 | C2 | semidirect |
| 7. #11720266 | C2 | semidirect |
| 101. #832 | D9 | semidirect |
| 213. C3×C9 | #490 | semidirect |
| 310. C9 | #5071 | semidirect |
| 354. C3 | #10588444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63502 | 2 |
| #11720935 | 2 |
| #11720576 | 2 |
| C9×#832 | 2 |
| #11720283 | 2 |
| #11720274 | 2 |
| #11720266 | 2 |
| #10591477 | 3 |
| #10588444 | 3 |