Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
374 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 89 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. C3×#63510 | C2 | semidirect |
| 3. #11720861 | C2 | semidirect |
| 4. C9×#837 | C2 | semidirect |
| 5. #11720286 | C2 | semidirect |
| 6. #11720261 | C2 | semidirect |
| 7. #11720258 | C2 | semidirect |
| 12. #88548 | C4 | semidirect |
| 13. #88547 | C4 | semidirect |
| 14. #88544 | C4 | semidirect |
| 15. #88543 | C4 | semidirect |
| 34. #63510 | D3 | semidirect |
| 111. #837 | D9 | semidirect |
| 233. C3×C9 | #444 | semidirect |
| 329. C9 | #5145 | semidirect |
| 367. C3 | #10588503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721868 | 2 |
| C3×#63510 | 2 |
| #11720861 | 2 |
| C9×#837 | 2 |
| #11720286 | 2 |
| #11720261 | 2 |
| #11720258 | 2 |
| #10591663 | 3 |
| #10588503 | 3 |