Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1596 conjugacy classes of subgroups; only the 515 normal subgroups are shown.
This group has 1596 conjugacy classes of subgroups — too many to draw. Only its 515 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 |
|---|---|---|
| 3. C2×#88853 | C2 | semidirect |
| 4. #11722188 | C2 | semidirect |
| 5. #11722186 | C2 | semidirect |
| 44. C22×C33 | Q16 | semidirect |
| 83. C22×C32 | Dic12 | semidirect |
| 95. C33 | #467 | semidirect |
| 122. C22×C3 | #3746 | semidirect |
| 129. C32 | #5116 | semidirect |
| 147. C22 | #88853 | semidirect |
| 154. C3 | #10592815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×C8 | 2 |
| #11723965 | 2 |
| C2×#88853 | 2 |
| #11722188 | 2 |
| #11722186 | 2 |
| #10592815 | 3 |