Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1540 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 459 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. #11722187 | C2 | semidirect |
| 5. #11722186 | C2 | semidirect |
| 92. C33 | #470 | semidirect |
| 124. C32 | #5137 | semidirect |
| 147. C3 | #10592836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×M16 | 2 |
| #11723965 | 2 |
| C2×#88853 | 2 |
| #11722187 | 2 |
| #11722186 | 2 |
| #10592836 | 3 |