Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1148 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 222 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 |
|---|---|---|
| 1. C22×C3×#634 | C2 | semidirect |
| 3. C2×C3×#3744 | C2 | semidirect |
| 4. C33×C22⋊C8 | C2 | semidirect |
| 5. C3×#63643 | C2 | semidirect |
| 6. #10592437 | C3 | direct (N × H) |
| 19. C22×#634 | C2×C3 | semidirect |
| 22. C2×#3744 | C2×C3 | semidirect |
| 26. C32×C22⋊C8 | D3 | semidirect |
| 27. C32×C22⋊C8 | C2×C3 | semidirect |
| 28. #63643 | C2×C3 | semidirect |
| 42. C3×#634 | D4 | semidirect |
| 72. C22×C33 | SD16 | semidirect |
| 89. C3×C22⋊C8 | C3×D3 | semidirect |
| 90. C3×C22⋊C8 | C3⋊D3 | semidirect |
| 113. #634 | C3×D4 | semidirect |
| 163. C22×C32 | #204 | semidirect |
| 164. C22×C32 | C3×SD16 | semidirect |
| 187. C22⋊C8 | C3×C3⋊D3 | semidirect |
| 188. C33 | #448 | semidirect |
| 258. C22×C3 | C3×#204 | semidirect |
| 259. C22×C3 | #3744 | semidirect |
| 276. C32 | #4738 | semidirect |
| 277. C32 | C3×#448 | semidirect |
| 311. C22 | C3×#3744 | semidirect |
| 318. C3 | C3×#4738 | semidirect |
| 319. C3 | #10592437 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#634 | 2 |
| C3×#64139 | 2 |
| C2×C3×#3744 | 2 |
| C33×C22⋊C8 | 2 |
| C3×#63643 | 2 |
| #10592437 | 3 |
| C3×#4738 | 3 |