Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
776 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11722389 | C2 | direct (N × H) |
| 3. C2×C3⋊#3688 | C2 | semidirect |
| 9. C3⋊#3688 | C22 | semidirect |
| 215. C2×C3 | #63690 | semidirect |
| 226. C3 | C2×#63690 | semidirect |
| 229. C2 | #11722389 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#41⋊C9 | 2 |
| #11722389 | 2 |
| C2×C3⋊#3688 | 2 |
| C2×#64160 | 3 |
| C2×#63690 | 3 |
| C2×#6226 | 4 |