Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
516 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 516 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. #11721866 | C2 | semidirect |
| 3. #11720964 | C2 | semidirect |
| 4. #11720891 | C2 | semidirect |
| 5. C3×#63396 | C2 | semidirect |
| 6. #11720301 | C2 | semidirect |
| 7. #11720296 | C2 | semidirect |
| 11. C2×#6226 | C22 | semidirect |
| 21. #88532 | C22 | semidirect |
| 22. C3×C4×Dic9 | C22 | semidirect |
| 23. C3×#3667 | C22 | semidirect |
| 40. #63396 | D3 | semidirect |
| 101. C4×Dic9 | C2×D3 | semidirect |
| 104. #3667 | C2×D3 | semidirect |
| 267. C3×C9 | #455 | semidirect |
| 383. C9 | #4825 | semidirect |
| 432. C3 | #10588921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#1009 | 2 |
| #11721866 | 2 |
| #11720964 | 2 |
| #11720891 | 2 |
| C3×#63396 | 2 |
| #11720301 | 2 |
| #11720296 | 2 |
| #10591688 | 3 |
| #10588921 | 3 |