Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
486 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 486 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. #11720924 | C2 | semidirect |
| 4. #11720891 | C2 | semidirect |
| 5. C3×#63396 | C2 | semidirect |
| 6. #11720301 | C2 | semidirect |
| 7. #11720299 | C2 | semidirect |
| 40. #63396 | D3 | semidirect |
| 260. C3×C9 | #456 | semidirect |
| 370. C9 | #4826 | semidirect |
| 415. C3 | #10588925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#1010 | 2 |
| #11721866 | 2 |
| #11720924 | 2 |
| #11720891 | 2 |
| C3×#63396 | 2 |
| #11720301 | 2 |
| #11720299 | 2 |
| #10591689 | 3 |
| #10588925 | 3 |