Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
532 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 532 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×#63497 | C2 | semidirect |
| 3. #11721265 | C2 | semidirect |
| 4. #11720577 | C2 | semidirect |
| 5. #11720332 | C2 | semidirect |
| 11. C22×C3×Dic9 | C22 | semidirect |
| 15. #88551 | C22 | semidirect |
| 17. C3×#3676 | C22 | semidirect |
| 28. #63497 | D3 | semidirect |
| 72. C22×Dic9 | C2×D3 | semidirect |
| 77. #3676 | C2×D3 | semidirect |
| 217. C3×C9 | #458 | semidirect |
| 321. C9 | #5053 | semidirect |
| 368. C3 | #10588923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#1004 | 2 |
| C3×#63497 | 2 |
| #11721265 | 2 |
| #11720577 | 2 |
| #11720332 | 2 |
| #10591533 | 3 |
| #10588923 | 3 |