Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
936 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 229 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. #11724517 | C2 | direct (N × H) |
| 3. C2×#88989 | C2 | semidirect |
| 4. C2×#88988 | C2 | semidirect |
| 13. #88989 | C22 | semidirect |
| 14. #88988 | C22 | semidirect |
| 75. C2×C33 | #131 | semidirect |
| 111. C33 | C2×#131 | semidirect |
| 134. C2×C32 | #948 | semidirect |
| 163. C32 | C2×#948 | semidirect |
| 178. C2×C3 | #64289 | semidirect |
| 189. C3 | C2×#64289 | semidirect |
| 191. C2 | #11724517 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3832 | 2 |
| #11724517 | 2 |
| C2×#88989 | 2 |
| C2×#88988 | 2 |
| C2×#64289 | 3 |
| C2×#948 | 9 |