Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
620 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 93 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×#63486 | C2 | semidirect |
| 3. C2×#88418 | C2 | semidirect |
| 4. C2×#88416 | C2 | semidirect |
| 5. C9×#830 | C2 | semidirect |
| 6. #11720284 | C2 | semidirect |
| 7. #11720277 | C2 | semidirect |
| 34. #63486 | D3 | semidirect |
| 121. #830 | D9 | semidirect |
| 264. C3×C9 | #452 | semidirect |
| 385. C9 | #5047 | semidirect |
| 434. C3 | #10588415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88736 | 2 |
| C3×#63486 | 2 |
| C2×#88418 | 2 |
| C2×#88416 | 2 |
| C9×#830 | 2 |
| #11720284 | 2 |
| #11720277 | 2 |
| #10591184 | 3 |
| #10588415 | 3 |