Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
848 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 142 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. C2×C3×#3746 | C2 | semidirect |
| 4. C32×#819 | C2 | semidirect |
| 5. #11722029 | C2 | semidirect |
| 20. C2×#3746 | D3 | semidirect |
| 28. C3×#819 | D3 | semidirect |
| 87. #819 | C3⋊D3 | semidirect |
| 173. C33 | #473 | semidirect |
| 244. C32 | #4896 | semidirect |
| 245. C32 | #5192 | semidirect |
| 274. C3 | #10590933 | semidirect |
| 275. C3 | #10592595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723942 | 2 |
| C2×C3×#3746 | 2 |
| #11723387 | 2 |
| C32×#819 | 2 |
| #11722029 | 2 |
| #10592595 | 3 |
| #10590933 | 3 |