Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
896 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 190 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. C33×#131 | C2 | semidirect |
| 2. C3×#64158 | C2 | semidirect |
| 3. C2×C3×#3745 | C2 | semidirect |
| 4. C3×#63650 | C2 | semidirect |
| 5. C3×#63646 | C2 | semidirect |
| 6. #10592841 | C3 | direct (N × H) |
| 20. C32×#131 | D3 | semidirect |
| 21. C32×#131 | C2×C3 | semidirect |
| 22. #64158 | C2×C3 | semidirect |
| 23. C2×#3745 | C2×C3 | semidirect |
| 26. #63650 | C2×C3 | semidirect |
| 27. #63646 | C2×C3 | semidirect |
| 81. C3×#131 | C3×D3 | semidirect |
| 82. C3×#131 | C3⋊D3 | semidirect |
| 174. #131 | C3×C3⋊D3 | semidirect |
| 177. C33 | #472 | semidirect |
| 252. C32 | #5142 | semidirect |
| 253. C32 | C3×#472 | semidirect |
| 285. C3 | C3×#5142 | semidirect |
| 286. C3 | #10592841 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#131 | 2 |
| C3×#64158 | 2 |
| C2×C3×#3745 | 2 |
| C3×#63650 | 2 |
| C3×#63646 | 2 |
| #10592841 | 3 |
| C3×#5142 | 3 |