Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
517 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 517 conjugacy classes of subgroups — too many to draw. Only its 61 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. H(3,𝔽3)×#100 | C2 | semidirect |
| 3. #11720580 | C2 | semidirect |
| 5. C23×#272 | C4 | semidirect |
| 10. #88552 | C4 | semidirect |
| 13. C32×#100 | D3 | semidirect |
| 99. #100 | #272 | semidirect |
| 101. H(3,𝔽3) | AΣL(1,𝔽16) | semidirect |
| 162. C32 | #4475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721847 | 2 |
| H(3,𝔽3)×#100 | 2 |
| #11720580 | 2 |
| C3×#4475 | 3 |