Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1316 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1316 conjugacy classes of subgroups — too many to draw. Only its 229 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. C33×#100 | C2 | semidirect |
| 3. #11722204 | C2 | semidirect |
| 5. C23×C3⋊(C3⋊D3) | C4 | semidirect |
| 10. #88864 | C4 | semidirect |
| 13. C32×#100 | D3 | semidirect |
| 48. C3×#100 | C3⋊D3 | semidirect |
| 88. #100 | C3⋊(C3⋊D3) | semidirect |
| 90. C33 | AΣL(1,𝔽16) | semidirect |
| 127. C32 | #4475 | semidirect |
| 157. C3 | #10589341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723978 | 2 |
| C33×#100 | 2 |
| #11722204 | 2 |
| #10589341 | 3 |