Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2100 conjugacy classes of subgroups; only the 635 normal subgroups are shown.
This group has 2100 conjugacy classes of subgroups — too many to draw. Only its 635 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 |
|---|---|---|
| 4. #11722186 | C2 | semidirect |
| 10. C2×#6308 | C4 | semidirect |
| 96. C33 | #419 | semidirect |
| 131. C32 | #5120 | semidirect |
| 155. C3 | #10592819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6308 | 2 |
| C2×C33×M16 | 2 |
| #11723967 | 2 |
| #11722186 | 2 |
| #10592819 | 3 |