Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
588 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 116 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. D3×#3746 | C2 | semidirect |
| 3. #11722199 | C2 | semidirect |
| 4. C3×#63656 | C2 | semidirect |
| 5. #11722009 | C2 | semidirect |
| 6. #11722007 | C2 | semidirect |
| 7. #11722001 | C2 | semidirect |
| 28. #63656 | D3 | semidirect |
| 174. C33 | #510 | semidirect |
| 236. C32 | #4918 | semidirect |
| 237. C32 | #5195 | semidirect |
| 264. C3 | #10591042 | semidirect |
| 265. C3 | #10592894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#919 | 2 |
| D3×#3746 | 2 |
| #11722199 | 2 |
| C3×#63656 | 2 |
| #11722009 | 2 |
| #11722007 | 2 |
| #11722001 | 2 |
| #10592894 | 3 |
| #10591042 | 3 |