Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1456 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1456 conjugacy classes of subgroups — too many to draw. Only its 351 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 |
|---|---|---|
| 3. C33×#103 | C2 | semidirect |
| 4. #11722205 | C2 | semidirect |
| 6. #11722188 | C2 | semidirect |
| 7. #11722177 | C2 | semidirect |
| 22. C32×#103 | D3 | semidirect |
| 66. C3×#103 | C3⋊D3 | semidirect |
| 117. #103 | C3⋊(C3⋊D3) | semidirect |
| 119. C33 | #484 | semidirect |
| 160. C32 | #4811 | semidirect |
| 190. C3 | #10592510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723987 | 2 |
| C4⋊C4×C3⋊(C3⋊D3) | 2 |
| C33×#103 | 2 |
| #11722205 | 2 |
| #11722190 | 2 |
| #11722188 | 2 |
| #11722177 | 2 |
| #10592510 | 3 |