Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
374 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 91 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. C9×#948 | C2 | semidirect |
| 3. #11720862 | C2 | semidirect |
| 4. C3×#63396 | C2 | semidirect |
| 5. #11720292 | C2 | semidirect |
| 6. #11720286 | C2 | semidirect |
| 7. #11720274 | C2 | semidirect |
| 12. #88548 | C4 | semidirect |
| 13. #88547 | C4 | semidirect |
| 14. #88544 | C4 | semidirect |
| 15. #88543 | C4 | semidirect |
| 36. #63396 | D3 | semidirect |
| 107. #948 | D9 | semidirect |
| 233. C3×C9 | #444 | semidirect |
| 329. C9 | #4823 | semidirect |
| 367. C3 | #10588825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721868 | 2 |
| C9×#948 | 2 |
| #11720862 | 2 |
| C3×#63396 | 2 |
| #11720292 | 2 |
| #11720286 | 2 |
| #11720274 | 2 |
| #10591663 | 3 |
| #10588825 | 3 |