Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
936 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 280 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. C3×#64289 | C2 | direct (N × H) |
| 3. C2×C3×#3788 | C2 | semidirect |
| 4. C2×C3×#3787 | C2 | semidirect |
| 5. C2×#64289 | C3 | direct (N × H) |
| 13. C3×#3788 | C22 | semidirect |
| 14. C3×#3787 | C22 | semidirect |
| 17. #64289 | C2×C3 | direct (N × H) |
| 18. C2×#3788 | C2×C3 | semidirect |
| 19. C2×#3787 | C2×C3 | semidirect |
| 43. #3788 | C22×C3 | semidirect |
| 44. #3787 | C22×C3 | semidirect |
| 75. C2×C33 | #131 | semidirect |
| 111. C33 | C2×#131 | semidirect |
| 134. C2×C32 | C3×#131 | semidirect |
| 163. C32 | C2×C3×#131 | semidirect |
| 178. C2×C3 | #64289 | direct (N × H) |
| 189. C3 | C2×#64289 | direct (N × H) |
| 191. C2 | C3×#64289 | 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 |
| C3×#64289 | 2 |
| C2×C3×#3788 | 2 |
| C2×C3×#3787 | 2 |
| C2×#64289 | 3 |
| C2×C3×#131 | 9 |