Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
342 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11720970 | C2 | semidirect |
| 3. #11720582 | C2 | semidirect |
| 4. C3×#63395 | C2 | semidirect |
| 7. #11720258 | C2 | semidirect |
| 32. #63395 | D3 | semidirect |
| 201. C3×C9 | #489 | semidirect |
| 287. C9 | #4794 | semidirect |
| 325. C3 | #10588734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#947 | 2 |
| #11720970 | 2 |
| #11720582 | 2 |
| C3×#63395 | 2 |
| #11720295 | 2 |
| #11720294 | 2 |
| #11720258 | 2 |
| #10591624 | 3 |
| #10588734 | 3 |