Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
250 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×C3⋊#3771 | C2 | semidirect |
| 3. #11724238 | C2 | direct (N × H) |
| 10. C3⋊#3771 | C22 | semidirect |
| 54. C2×C33 | M32 | semidirect |
| 81. C33 | C2×M32 | semidirect |
| 100. C2×C32 | #812 | semidirect |
| 126. C32 | C2×#812 | semidirect |
| 140. C2×C3 | #64214 | semidirect |
| 151. C3 | C2×#64214 | semidirect |
| 153. C2 | #11724238 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3787 | 2 |
| C2×C3⋊#3771 | 2 |
| #11724238 | 2 |
| C2×#64214 | 3 |
| C2×#812 | 9 |