Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2604 conjugacy classes of subgroups; only the 863 normal subgroups are shown.
This group has 2604 conjugacy classes of subgroups — too many to draw. Only its 863 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 |
|---|---|---|
| 12. C2×#6308 | C4 | semidirect |
| 30. C2×C3⋊(C3⋊Dic3) | Q8 | semidirect |
| 96. C33 | #391 | semidirect |
| 133. C32 | #4973 | semidirect |
| 161. C3 | #10592672 | 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×C4⋊C4 | 2 |
| C2×C4×C3⋊(C3⋊Dic3) | 2 |
| #11722201 | 2 |
| #10592672 | 3 |