Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
499 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 499 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#3744⋊C3 | C2 | semidirect |
| 3. C2×#3746⋊C3 | C2 | semidirect |
| 4. #64084⋊C3 | C2 | semidirect |
| 5. C4×C8×H(3,𝔽3) | C2 | semidirect |
| 6. #10592395 | C3 | semidirect |
| 17. C2×#3746 | C2×C3 | semidirect |
| 19. C2×#3744 | C2×C3 | semidirect |
| 20. #64084 | C2×C3 | semidirect |
| 26. C32×C4×C8 | D3 | semidirect |
| 27. C32×C4×C8 | C2×C3 | semidirect |
| 165. C4×C8 | (C3⋊D3)⋊C3 | semidirect |
| 166. H(3,𝔽3) | #495 | semidirect |
| 244. C32 | #4696 | semidirect |
| 245. C32 | C3×#495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3745⋊C3 | 2 |
| C2×#3744⋊C3 | 2 |
| C2×#3746⋊C3 | 2 |
| #64084⋊C3 | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| #10592395 | 3 |
| C3×#4696 | 3 |