Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1624 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1624 conjugacy classes of subgroups — too many to draw. Only its 258 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. C32×#935 | C2 | semidirect |
| 3. C32×#834 | C2 | semidirect |
| 5. C3×#5243 | C3 | direct (N × H) |
| 9. C22×C32×Dic3 | C22 | semidirect |
| 11. C32×#217 | C22 | semidirect |
| 17. C3×#935 | C2×C3 | semidirect |
| 19. C3×#834 | C2×C3 | semidirect |
| 31. #5243 | C32 | direct (N × H) |
| 42. C22×C3×Dic3 | C22×C3 | semidirect |
| 47. C3×#217 | C22×C3 | semidirect |
| 61. #935 | C2×C32 | semidirect |
| 63. #834 | C2×C32 | semidirect |
| 106. C22×Dic3 | C22×C32 | semidirect |
| 111. #217 | C22×C32 | semidirect |
| 138. C33 | #458 | semidirect |
| 206. C32 | #5243 | direct (N × H) |
| 207. C32 | C3×#458 | semidirect |
| 236. C3 | C3×#5243 | direct (N × H) |
| 237. C3 | C32×#458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×H(5,𝔽2) | 2 |
| C32×#935 | 2 |
| C32×#834 | 2 |
| C32×#458 | 3 |
| C3×#5243 | 3 |